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The University of Connecticut 
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BOOK 54 1.345.D92 c. 1 

OU NOUY # SURFACE EQUILIBRIA OF 

BIOLOGICAL AND ORGANIC COLLOIDS 



3 ^153 00132^2=1 1 



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http://archive.org/details/surfaceequilibriOOIeco 



SURFACE EQUILIBRIA OF 

BIOLOGICAL AND ORGANIC 

COLLOIDS 



BY 

P. LECOMTE DU NOUY, D.Sc. 

INTRODUCTIONS 
BY 

Dr. ALEXIS CARREL 

AND 

Prof. ROBERT A. MILLIKAN 




American Chemical Society 
Monograph Series 



BOOK DEPARTMENT 
The CHEMICAL CATALOG COMPANY, Inc. 

19 EAST 24th STREET, NEW YORK, U. S. A. 
1926 









Copyright, 1926, by 
The CHEMICAL CATALOG COMPANY, Inc. 



All rights reserved 



Printed in the United States of America by 

J. J. LITTLE AND IVES COMPANY, NEW YORK 



GENERAL INTRODUCTION 

American Chemical Society Series of 
Scientific and Technologic Monographs 

By arrangement with the Interallied Conference of Pure and 
Applied Chemistry, which met in London and Brussels in July, 
1919, the American Chemical Society was to undertake the pro- 
duction and publication of Scientific and Technologic Mono- 
graphs on chemical subjects. At the same time it was agreed 
that the National Research Council, in cooperation with the 
American Chemical Society and the American Physical Society, 
should undertake the production and publication of Critical 
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Chemical Society and the National Research Council mutually 
agreed to care for these two fields of chemical development. 
The American Chemical Society named as Trustees, to make 
the necessary arrangements for the publication of the mono- 
graphs, Charles L. Parsons, Secretary of the American Chemical 
Society, Washington, D. C.J John E. Teeple, Treasurer of the 
American Chemical Society, New York City; and Professor 
Gellert Alleman of Swarthmore College. The Trustees have 
arranged for the publication of the American Chemical Society- 
series of (a) Scientific and (b) Technologic Monographs by the 
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The Council, acting through the Committee on National Policy 
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The editors of each series will endeavor to select topics which 
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3 



4 GENERAL INTRODUCTION 

The development of knowledge in all branches of science, and 
especially in chemistry, has been so rapid during the last fifty 
years and the fields covered by this development have been so 
varied that it is difficult for any individual to keep in touch with 
the progress in branches of science outside his own specialty. 
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Consequently when men who have spent years in the study of 
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and present it in concise, readable form, they perform a service 
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It was with a clear recognition of the usefulness of reviews of 
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Two rather distinct purposes are to be served by these mono- 
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critical selection will be made of those papers which are most 
important. 



GENERAL INTRODUCTION 5 

The publication of these books marks a distinct departure in 
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tance of the enterprise and take sufficient interest to justify it. 



AMERICAN CHEMICAL SOCIETY 



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C. E. K. Mees, 

F. W. WlLLARD. 



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To The Memory of 
MY MOTHER 



.FOREWORD 

The following work is an experimental study of surface phenomena 
observed in biological and organic colloids. So far as we know, nothing 
has yet been published on the study of the static surface tension of 
colloidal solutions. A very large number of measurements of both 
dynamic and static surface tension have been made in our laboratory 
by different experimenters ; the most important results obtained are 
described. A method was developed which was thought to be an 
improvement on those used heretofore and which made it possible to 
disclose a number of facts overlooked until now because of the lack of 
proper technique. This book must be regarded as a description of 
this method, followed by a few examples of its application to the 
study of surface equilibrium of colloidal solutions, rather than as a 
complete survey of this field. 

Only a very small number of the problems which can be attacked by 
this method have been studied. Some of the experimental results 
obtained do not harmonize with certain modern theories, and the 
writer's interpretations may be discussed on the basis of these theories, 
but they are given in order to explain new facts for which the existing 
hypotheses do not seem to afford a completely satisfactory and quan- 
titative explanation. Until a new hypothesis is offered, or contradictory 
phenomena are found, it would seem that the proposed interpretation 
can be retained. 

A theory is merely a stepping stone and should be discarded as 
soon as it is unable to account for all phenomena. The phenomena 
reported in this book are easy to observe under the proper conditions, 
and even assuming that their interpretation is wrong, they themselves 
will remain untouched and will have to be taken into account. 

In ending this foreword I wish to express my gratitude to Dr. Simon 
Flexner, Director of the Rockefeller Institute, for the facilities extended 
to me ; to Dr. Alexis Carrel for his unfailing and inspiring encourage- 
ment and his kindness in presenting this book to the biologists ; to Prof. 
Robert A. Millikan, who was good enough to devote part of his valuable 
time to write an introduction for the physicists ; to Dr. Michael Heidel- 

ii 



12 FOREWORD 

berger, who took the trouble to read and correct the proofs; to Dr. 
Lillian E. Baker, who collaborated in many ways and prepared or 
supervised the preparation of the pure chemicals which were used; 
to Mr. John Zwick, my technical assistant, who performed an important 
part of the experimental work, and not least to my wife, who translated 
the book into English and helped me in its preparation. 

P. Lecomte du Nouy, 

Laboratories of the Rockefeller Institute, 

New York, 1925-1926. 



INTRODUCTION 

Doctor Alexis Carrel 

I have followed with great interest the experiments of Dr. du Noiiy, 
both on account of their intrinsic value and their bearing on important 
biological problems. In the investigation of the properties of the tissues 
and the fluids of the organism, there is need of new methods and new 
hypotheses. Although the relations of the living cells and of the 
molecular aggregates of the humors are overwhelmingly complex, the 
fundamental laws of which they are an expression will be discovered. 
But proper methods must be applied. Dr. du Nouy has had the courage 
to give up the study of the comparatively simple problems which deal 
exclusively with inanimate matter, and to blaze a trail through the 
jungle of physiological phenomena. His explorations have already 
brought forth important new facts, brilliant hypotheses, and the prospect 
of future discoveries. Every biologist will read this book with profit 
and will enjoy the fascinating ingeniousness of the conceptions and 
the methods of its author. 

Alexis Carrel, 
The Rockefeller Institute for 
Medical Research, 
New York, May 13, 1926. 



INTRODUCTION 

Prof. Robert A. Millikan 

I have read the manuscript of Dr. du Noiiy's book with very great 
interest. From the standpoint of the physicist it is notable from two 
points of view. First, it makes an important contribution to Physics 
itself. The discovery that in a solution the establishment of equilibrium 
conditions — the only conditions in which the Gibbs thermodynamic 
equation is valid — is a slow process, capable of being followed step by 
step, is an important one. It gives us pause in the matter of drawing 
hasty conclusions from that law. Second, it is very stimulating to see 
what a wealth of new applications can still be found for an old physical 
method, and what a flood of new light may still be thrown upon complex 
'processes by the intelligent use of an old instrument, refined in its 
details, but not different in principle from the one which is used in a 
freshman laboratory. Dr. du Noiiy's book will interest every student of 
molecular physics. 

Robert A. Millikan, 

Norman Bridge Laboratory of Physics, 
California Institute of Technology, 
Pasadena, California. 

May, 1926. 



TABLE OF CONTENTS 

PAGE 

Chapter 1. Technique 19 

Introduction. The Tensiometer. Standardisation. Absolute 
Measurements. Relative Measurements. Preparation of the 
Glasses. Wetting of the Glass. Preparation of the Solu- 
tions. Experimental Set-up. 

Chapter 2. Drop of the Surface Tension of Colloidal Solutions as a 

Function of Time 35 

Technique. Application to the study of serum solutions and 
sodium oleate. Action of Stirring. Action of Heat on the 
Surface Tension of Serum. Influence of Gases on the. Sur- 
face Tension of Serum solutions. 

Chapter 3. Monomolecular Layer of Serum Constituents . . . . 71 
Adsorption on the Glass. Percentage of Proteins in Rabbit 
Serum. Specific Gravity of Anhydrous Proteins. Calcula- 
tion of the thickness of the monolayer. Significance of the 
Critical Concentration. 

Chapter 4. Sodium Oleate 86 

Dimensions of the Molecule. Calculation of the Constant 
N of Avogadro. Discussion of the Errors. 

Chapter 5. Egg Albumin 105 

Study of the Egg Albumin Molecule. Dimensions. Molec- 
ular weight. 

Chapter 6. Characteristics of Immune Serum 121 

Chapter 7. Influence of Colloids on the Crystallization of Sodium 

Chloride 145 

Aspects of Crystals after evaporation. Aspects of Crystals 
at the Critical Concentrations: 1. Sodium Oleate Monolayers. 
2. Immune Serum. 

Chapter 8. Surface Equilibrium of Complex Colloidal Solutions . . 155 
Antagonistic Effect. — A highly sensitive Method for detect- 
ing Proteins and Colloidal Particles in a Solution. 

Chapter 9. Interfactal Tension. Instrument — Results — Temperature 
Coefficient— Adsorption at Interfaces as a Function of Time. 
Surface Viscosity. — Its Increase with Time 166 

Chapter 10. Colloidality of Solutions of Proteins, Serum and Plasma 178 

Chapter 11. General Conclusions 187 

Table of Figures and Plates 203 

Name Index ' 207 

Subject Index 209 



Chapter I. 
Technique. 

Introduction. 

A survey of the advancement of knowledge brings the realisation that 
the progress of science has been achieved through the constant improve- 
ment of experimental technique. 1 This, of course, does not apply to the 
immense strides made by the speculative genius of men like Newton, 
Maxwell and Einstein, who belong in a class apart. 

This fact is so self-evident that it is unnecessary to illustrate it by 
any examples. The starting point of a great discovery is often due to 
chance; that chance which, according to Pasteur, "only favors those 
whose minds are prepared." But no matter how important, such a 
chance is no more than a starting point and the future of the discovery 
depends on the ability of the observer to conceive and put into practice 
the methods which will enable him to dissect the phenomenon, to link 
it up with facts already known and to forge ahead. 

Next to the important problem of the establishment of a technique is 
that of the "choice of approximation," which depends not only on a thor- 
ough scientific culture but on the common sense of the scientist. The 
choice of approximation consists in proportioning the precision of the 
measurement to the precision of the experiment. It is obviously of 
no interest to quote the second decimal figure if the experimental 
errors occur in the first. But even in contemporary scientific literature 
examples are easily found in which the surface tension of colloidal 
solutions, for instance, is expressed to 0.01 dynes. Whoever has had 
any experience of these measurements must realise that this is an 
artificial precision with no real significance. 

1 "Experimental criticism must be founded by creating rigorous methods of 
investigation and experimentation which will render the observations unques- 
tionable and will eventually suppress the errors in the facts which are the source 
of errors in theory. The real promoter of scientific knowledge at present will 
be he who can bring some principle of simplification into analytical procedure, or 
improvements into the research apparatus. I am convinced that in the experi- 
mental sciences which are in evolution, and particularly in those as complex as 
biology, the discovery of a new instrument of observation or of experimentation 
renders much more service than many systematical or philosophical dissertations." 
These lines were written by Claude Bernard, in his admirable book, "Introduction 
a I' etude de la mhdecine expcrimentale" (4th Ed. pp. 272-273). 

19 



20 SURFACE EQUILIBRIA 

In order to obtain a correct measurement it is indispensable to 
possess a knowledge of all the factors susceptible of influencing the 
principal phenomenon and one cannot be too particular in this matter. 
If the extent to which a phenomenon is affected by the different con- 
ditions necessary for its evolution (temperature, pressure, time, etc.) 
is unknown, it is essential to control these variables with the utmost 
care, for it is evident that in certain cases the errors could be additive 
and attain an order of magnitude similar to that of the main phenome- 
non. When a better knowledge of the subject makes it possible to as- 
sume its relative independence of certain factors, the same strictness in 
the control, so far as the latter are concerned, is no longer required. A 
rigorous accuracy in the conditions of the experiment, and in the final 
measurement a proper proportion to the order of magnitude of the 
sum of errors, such are the rules imposed by logic and experience. 

An example will make this clear. Supposing a certain phenomenon 
A is to be studied. This phenomenon is dependent on the factors a, b, 
c, d. The proportion of the error in the measurement of A which can 
be attributed to each of these factors respectively is unknown. It is 
evident that the accuracy in the measurement of A depends on the 
accuracy with which a, b, c, d can be estimated, and that the greater 
the number of factors the closer this estimation must be. For, sup- 
posing that the errors involved in the technique employed in the deter- 
mination of A amount to one per cent and that the values of the four 
principal factors a, b, c, d are known with the same degree of approxi- 
mation, if it happens that these errors are additive, the value of A will 
show an error of five per cent. Thus the advantage of disposing of 
a technique for measuring A with an error of only one per cent becomes 
illusory. To obtain the full benefit of this advantage it is therefore 
necessary to carry precision to the extreme limit so far as the measure- 
ments and control of the four principal factors of the phenomenon are 
concerned, so that the sum of the possible errors involved in this deter- 
mination in no case exceeds one per cent. 

About 125,000 measurements of colloidal solutions have been made in 
our laboratory during the past five years. We shall insist in the course 
of this chapter on the imperative necessity of certain meticulous tech- 
nical procedures, the importance of which has been gradually realised. 
However, only the first decimal of the values of surface tension will 
be mentioned in this book, for it has been our experience that even 
when all these precautions are taken, it is impossible to reach a greater 
degree of precision. 



TECHNIQUE 21 

The Tensiometer. 

It may be of interest to review the reasons which definitely deter- 
mined the adoption of the ring method and led to the development of 
the tensiometer. 2 

There are about twenty different methods for the measurement of 
the surface tension of liquids. These methods have been reviewed 
in detail by A. Ferguson, 3 who clearly demonstrates, in a remarkably 
thorough paper, that only three need be considered; the so-called 
Jaeger method, 4 the method based on the photography of large air- 
bubbles produced in the liquid, and the ring method. 

Speaking generally, the methods can be divided into two principal 
categories : those which depend on a knowledge of the angle of contact 
and those which do not. Those which depend on it are unsatisfactory 
when applied to colloids. 5 The others may be divided again into two 
principal classes if one considers them from the special standpoint of 
colloidal solutions : 1st, the dynamic methods ; 2nd, the static methods. 

The difference in the values obtained by these two classes of methods 
had been noted, but no practical conclusion had been drawn until the 
basic phenomenon on which the present work is founded was put in 
evidence. 6 It was universally admitted that adsorption into the sur- 
face layer of substances capable of diminishing the surface tension 
of water, according to Gibbs' law, 7 was instantaneous. One exception 
was, however, observed : that of sodium oleate, which has a considerable 
action on the surface tension of water. For this substance a large 
difference was found between the static and dynamic values. Accord- 
ing to Bayliss a 0.025 per cent solution has a static surface tension of 
26 dynes and a dynamic one of 79 (?) dynes. Bayliss seems to have 
been the only one to note this fact and to deduce the following con- 

2 Lecomte du Noiiy. J. of Gen. Physiol. 1918-1919, I, 521. W. M. Bayliss. 
The Colloidal State, Oxford Med. Publ. London, 1922, p. 65. H. N. Holmes, 
Laboratory Manual of Colloid Chem. N. Y. Wiley. 1925, p. 50 and following. 
H. Vigneron, Precis de Chimie Physique, Mass'on, Paris, 1924, p. 45. 

3 Allan Ferguson. Science Progress, 1914-15, Vol. IX, p. 428. 

4 O. D. Chwolson. Traite de Physique, Hermann, Paris, 1907, Vol. I. Fasc. 
1, p. 525. 

6 The capillary ascension, and the hanging drop or drop weight methods are 
included in this category. Although the latter has given satisfactory results in 
the case of pure liquids, it is absolutely unreliable in the case of colloidal solu- 
tions. This point will be explained and emphasized later on. (See pp. 22, 41 
and 42.) 

6 Lecomte du Noiiy. J. of Exp. Med. Spontaneous Decrease of the S. T. 
of Serum, April 1922, XXXV, p. 575. 

7 Willard Gibbs, on the Equilibrium of Lleterogeneous Substances. Trans. 
Conn. Acad. 1874-8, III, p. 380. Scientific papers, London, 1906. 



22 SURFACE EQUILIBRIA 

elusion : "the fact is interesting because it shows that the process of 
adsorption is not instantaneous although it is extremely rapid." 8 The 
problem was still at this point in 1920. As there was no practical 
method for measuring the static value, the surface tension of colloids in 
general and of proteins in particular had been studied very vaguely 
by means of methods involving serious causes of error. The idea that 
other colloids could act in the same manner as sodium oleate did not 
appear likely, because with the relatively concentrated solutions em- 
ployed (from 1/10 to 1/1,000 in general), the difference between the 
static and the dynamic values was slight and of nearly the same order 
of magnitude as the experimental errors (from 2 to 5 dynes/cm.). 
Consequently, though considerable literature exists on the surface ten- 
sion of blood serum, for example, the measurements are, with rare 
exceptions, without value and the conclusions most misleading. The 
most widely used methods until now have been the "stalagmometric" 
or drop weight methods. The main reasons why they are not well 
adapted to the measurement of the surface tension of colloidal solu- 
tions follow as a natural consequence of the experiments reported in 
Chapter 2. 

It will be shown, indeed, that as soon as a colloidal solution is allowed 
to stand undisturbed, the first rapid process of adsorption in the surface 
layer is followed by a slower one, which may last for hours and is very 
active during the first minutes. 

In case the dynamic or initial value of the surface tension is required, 
it is important to observe that the readings will differ according to the 
time which elapsed since the liquid was last stirred. The sooner the 
measurement is made, the higher the value. The same holds true if 
hanging drop methods are used ; the readings will differ according to 
the time required to form a drop. 

A glance at any of the curves expressing the decrease of the surface 
tension of such solutions — undiluted serum, for example — will make 
this very clear. Unless it is certain that with a given tip each drop 
will be formed in exactly the same time, it cannot be assumed that the 
reading is reproducible. Of course, mean values are taken, and the 
errors are thus minimised, but, nevertheless, the fact remains that this 
reading corresponds to an arbitrary value placed anywhere on the curve 
expressing the decrease as a function of the time (Figures 7 and 8). 
The error is much more important in the case of sodium oleate (Figure 
5). For this reason, it is not believed that initial values should be relied 
8 W. M. Bayliss. Principles of General Physiology, London, 1918, p. 56. 



TECHNIQUE 23 

upon. It seems more advisable to wait until equilibrium is attained, 
and then take a reading which corresponds to a static condition of the 
solution. The capillary tube methods are entirely unsuited as static 
methods because of the adsorption on the glass, the time required to 
make a reading, the difficulty encountered in the calibration of the 
capillary, and the important fact pointed out by Joh. Mathieu, (Ann. der 
Phys. IV, F.9 p. 340) concerning the decrease in the concentration 
which normally occurs in capillaries. There are also the technical 
difficulties of cleaning, reading, etc. 

Jaeger's method of capillary tubes not being a static method, and 
the method of air-bubbles being extremely difficult of realisation, there 
remained only the method of the tearing off of a ring, which was 
impractical as devised by Sondhaus, 9 Timberg, 10 and Weinberg, 11 in the 
form of a large copper ring suspended under the pan of a balance. 
This method, however, was easily improved and adapted to the neces- 
sities of our problem. The conditions to be fulfilled were : 

1. Employment of a small quantity of liquid. 

2. Great rapidity of measurement (about 20 seconds). 

3. Possibility of a large number of measurements in a short time. 

4. Elimination of systematic causes of error. 

5. Precision of the order of 1/10 of a dyne (that is 0.14 per cent 
for water and 0.3 per cent for alcohol and ether). 

6. Easy standardisation in absolute units (dynes/cm.). 

These six principal conditions imposed the dimensions of the actual 

instrument. The ring and supporting stirrup are made of platinum- 

iridium wire (10 to 15 per cent iridium), with all joints welded, so that 

any contaminations may be removed by flaming. The mean perimeter 

of the ring is 4 cm. zb 0.005 cm. This length is controlled at the 

factory by steel dies, the diameter of which is known to within 1/100 

of a millimeter. The diameter of the wire with which the ring is made 

is equal to 0.3 millimeters. The torsion wire is a fine steel piano wire 

(diameter 0.25 millimeters), secured at both ends in torsion heads, each 

of which is driven by a worm gear arrangement. The tension of this 

wire is weak but the readings are practically independent of it. Every 

experimenter must standardise his own instrument and the changes in 

tension due to fluctuations in temperature do not affect the readings 

to a measurable extent. The readings on the dial throughout the whole 

9 C. Sondhaus. Pogg. Ann., 1878, VIII, p. 27. 

10 Gustaf Timberg Ann. d. Phys. und Chem., 1887, XXX, 4, p. 545. 

11 Boris Weinberg. Zeitschrift fur Phys. Chem. 1902. X, p. 34. 



24 



SURFACE EQUILIBRIA 



range from to 100 arc proportional to the momentum; that is to say, 
a double weight placed on the ring should correspond to double the 
reading on the dial. The control should be made as it sometimes happens 




Courtesy Central Scientific Co., Chicago. 

Fig. 1. — View of the Tensiometer. 

that the figures do not correspond exactly owing to a slight imperfection 
in the wire, in which case the latter should be changed. (Fig. 1.) 

Standardisation. 

To calibrate the instrument in absolute units C. G. S. it is advisable 
to place it on a table at such a height that the eyes are on the same plane 
as the wire. In this way the determination of zero can be made with 
accuracy and ease. Then by turning the knurled head D at the far end 
of the torsion wire W, draw the latter up tightly so that it will not sag 
appreciably when a weight of, say 1 gr., is applied near its middle point, 
where the arm K is attached. By means of the knurled head A, set 
vernier V at the zero point of scale S. Then with stop Y so set that the 
upward motion of arm K is limited to six or eight millimeters above 
the index /, turn knurled head C until the arm K is in its zero-balance 
position. The zero-balance is established when the lower edge of the 
arm as viewed from the left side of the scale dial just appears to touch 
the apex of the indicator /. This can be easily judged since the white 
background sharply outlines the arm and the indicator, so that at the 
zero-balance position two narrow, white wedges appear between the 
index and the arm, with points just touching. This is shown in the 
small, enlarged view of the indicator. Then cut a small strip of paper 



TECHNIQUE 25 

and place it across the ring, and by means of knob C readjust the arm 
to its zero position. Place on the strip of paper an accurately known 
arbitrary weight of from 500 to 800 milligrams and turn the head A 
so that vernier V moves toward the right until the arm is again in the 
zero-balance position. Read the scale to 0.10 division, or if there is no 
coincidence between a line on the vernier and a line on the scale, 

estimate to 0.05. The formula is y (surface tension) = -~-j-, when M 

is the weight in grams placed on the ring (including the paper strip), 
g = 980.6 and L the length of the perimeter of the ring in cm. This 
figure is multiplied by 2 because two films are formed, one inside and 
one outside the ring, when pulled from the liquid. Let the observed 
reading be y and let M be the weight in grams which corresponds to 
this reading. Then 980.6 M (the value of g applying to the particular 
location should be used) represents the number of dynes of force 
exerted on the ring, which gives the reading y. The force of the film 
applied at the ring is then balanced by the torsion in the wire. When 
the instrument is in adjustment its reading should represent directly 
the number of dynes of force exerted by 1 cm. length of film. Since 
the torsion of the wire per degree of twist is constant over the entire 
scale, each scale division represents 1 dyne for each centimeter of film 

length applied at the ring. We therefore find that -~y- should be equal 

to y in order that the instrument may be direct reading. If this is not 
the case, adjust the vernier to the value of y on the scale which corre- 
sponds to -7zj- and then adjust the screw G until zero-balance of the arm 

is obtained. This adjustment of G has changed the amount of force 
applied at the ring since the length of the lever arm has been changed. 
Hence upon removal of the weight the zero-balance position of the arm 
will not correspond to the zero position of the vernier. Adjust the 
vernier to its zero position and bring the arm back to zero-balance by 
adjustment of knurled head C. Replace the weight, set the vernier at 
the same reading as before, and again adjust G if necessary. The 
process of adjusting G and the zero-balance position of the arm, with 
the weight removed and the vernier set at zero, should be repeated until 
no further adjustment is needed. This usually takes about ten minutes. 
(If only comparative results are required, as is generally the case for 
colloidal solutions in which variations in the surface tension are studied, 
it is, of course, unnecessary to adjust the instrument so exactly.) After 



26 SURFACE EQUILIBRIA 

the weight and paper have been removed from the ring the final adjust- 
ment is made by means of knurled head C, after which the instrument 
is ready for making absolute surface tension measurements, which will 
be indicated directly by the vernier on scale 5. 

Example of calibration for absolute measurements : 

Weight M = 0.700 gr. 
g = 980/6 
L— 3.99 cm. 

Y 2L 

0.700 X 980.6 



2 X 3.99 



86.45. 



The vernier is set at 86.45 and with the 700 milligram weights in 
position on the ring, screw G is adjusted until a zero-balance is obtained. 

Absolute Measurements. 

After having strictly observed the precautions given below for clean- 
ing everything with which the liquid is likely to come in contact, put a 
small portion of the liquid in a watch glass or other shallow vessel on the 
adjustable table T. The instrument is leveled until this table is approxi- 
mately horizontal by turning screws L and L' '. With screw B turned 
so that the table T is near its lowest position, adjust the table bracket by 
means of clamp screw P until the liquid is within 4 or 5 mm. of the 
ring. Move collar M up until it touches the bracket clamp and secure 
it in position. 

Wet the ring with the liquid by dipping it below the surface of the 
latter, and pull it away. Usually a number of minute drops will adhere 
to the ring. In some cases the ring will be uniformly wet. The weight 
of the adhering liquid would cause a reading somewhat too high. This 
error is automatically compensated by adjusting arm K to its zero- 
balance with the ring wet. A readjustment is necessary when liquids 
with a materially different specific gravity are used. 

Having adjusted the zero-balance of arm K, turn screw B so as to 
elevate the table until the surface of the liquid touches the ring. As 
a rule the ring will be drawn down into the liquid. With the right hand 
turn the head A so as to move the vernier up scale and at the same 
time, with the left hand, turn the micrometer adjusting screw B so as 
to lower the vessel containing the liquid, always keeping the arm in its 
position of zero-balance.. As the torsion in wire W approaches the 



TECHNIQUE 27 

value at which the film begins to form, turn both screws A and B very 
slowly and cautiously, taking care to maintain the zero-balance position 
of the arm. At the instant the film breaks, stop turning. The reading 
of the vernier then gives the surface tension of the liquid in dynes per 
centimeter. 

To minimise error in scale reading, be sure that arm K is in the 
zero-balance position at the moment of the rupture of the film. A rough 
preliminary measurement will indicate the order of magnitude of the 
surface tension of the liquid being studied. Under such conditions it 
is easy to see that the reading on the vernier corresponds to the 
effort in dynes/cm. required to break the equilibrium of the liquid 
film raised by the ring. When the point of rupture is attained it is 
evident that the reading is slightly above the tension of the liquid 
corresponding to the equilibrium. The error is of the order of 0.02 dyne 
for distilled water, that is to say, negligible, as the readings are only 
expressed to 0.1 dyne. On the other hand, this technique has the advan- 
tage of not leaving the estimation of the equilibrium to the judgment 
of the experimenter. The rupture is very sudden and the impact of 
the arm K against the stop Y making a noise which is heard almost 
simultaneously with the ring being torn from the liquid, the hand 
turning the knob is stopped by it almost automatically and more rapidly 
than if the experimenter depended only upon ocular reaction. Measure- 
ments made by untrained assistants were always found to agree within 
0.2 dyne. 

The values obtained with this technique are in perfect accord with 
those of the best authorities. These values, however, differ somewhat 
according to the methods and even for the same method when used 
by different experimenters. This is one of the reasons why the absolute 
value of the second decimal point is questionable. 

It should be noted that the values published by those who have used 
the ring method until now are decidedly higher. Timberg 12 gives a 
value of y = 77.91 at 20.8°, and Weinberg 13 y = 76.8 at 18°. Cantor, 14 
who advocates a very complicated formula, is the only one to give a 
value of y — 73.76, but without mentioning the temperature, so that 
this figure cannot be taken into consideration. This constant difference 
of about 3.2 dynes with the mean values obtained by the other methods 
remained inexplicable until P. E. Klopsteg 15 clearly showed that it 

" Timberg, loc. cit. 

18 Weinberg, loc. cit. 

14 M. Cantor, Ann. der Phys. u. Chem. 1892, XLVII, p. 399. 

18 P. E. Klopsteg. Science, 1924, LX. No. 1553, p. 319. 



28 



SURFACE EQUILIBRIA 



TABLE I. 

Surface Tension of Water at 18°. 
(From Freundlich's Kapillarchemie) 



Method 



Undulatory jet 



Vibrating drops 
Capillary waves 



Deformed surfaces 
Capillary ascension 
Adhesion of a disc. 
Drop weight 



Pressure in air bubbles 



Ring method (Tensiometer du Noiiy) 



Dynes/Cm. 


Experimenter 


73.0 


Rayleigh 


73.8 


Pedersen 


72.4 


Bohr 


73.0 


Lenard 


74.0 


Rayleigh 


73.3 


Dorsey 


73.8 


Kalahne 


73.5 


Lohnstein 


73.1 


Volkmann 


73.1 


Hall 


73.8 


Ollivier 


75.2 


Cantor 


73.7 


Magini 


72.7 


Jaeger 


73.7 


Klopsteg 


73.7 


du Noiiy 


73.7 


Zwick 



was due to an imperfect technique and could be easily remedied with 
the tensiometer. It is his technique which we have described above. 
Indeed, if the surface tension of water be measured with the tensiometer, 
by turning the knurled head A alone, that is to say without moving the 
table which carries the liquid, part of the effort of torsion of the wire 
is employed in raising the liquid and the rupture is not produced with 
the arm in a horizontal position but when the latter is decidedly above 
its zero-balance position. As the instrument is standardised with the 
arm at 0, this must necessarily result in a systematic error. Hence it 
suffices to lower the liquids progressively as the torsion of the wire is 
increased, and thus to maintain the arm horizontal to ensure correct 
readings in accord with the other methods. 

Relative Measurements. 

Measurements of the surface tension of water at 18°, for example, 
identical with those of Timberg and Weinberg, that is 76.8 dynes, can 
be obtained by only turning the knob without touching the table when 
the absolute value of surface tension is not required; that is, when, 
as is often the case, the variations of tension with respect to different 
factors are studied it is unnecessary to use the afore-mentioned tech- 
nique which takes more time. The liquid is raised until it is in contact 
with the ring and stays in that position during the measurement. The 
values are higher but the readings are comparable. 



TECHNIQUE 29 

An objection may be raised concerning the thickness of the ring; 
however, the results of experiments made both by ourselves and by 
Klopsteg show that when instead of a, circular ring 0.3 mm. thick, an 
aluminum or steel tube, with carefully sharpened and beveled edges, is 
used, the readings are identical. 

Preparation of Glasses. 
Wetting of the Glass. 

The importance of this part of the technique cannot be too strongly 
emphasised. Errors introduced in measurements through the use of 
glasses, pipettes and funnels which have been insufficiently cleaned or 
cleaned with alcohol or ether, can, in certain cases, amount to 30 per 
cent, whilst all other causes of error put together do not amount to five 
per cent. A difference of five degrees in the estimation of the tempera- 
ture of an aqueous solution does not involve an error of one dyne (e.g. 
1.4 per cent for water). It can be roughly estimated that around 20° 
each degree added or subtracted corresponds to a difference of 0.17 
dyne. It is, therefore, of fundamental importance to conform rigor- 
ously to the following indications, which are the result of several years' 
experience, if it be desired to obtain constant results or, at least, to 
eliminate the most prolific source of error. 

All glassware must be boiled for two hours at least, in a solution 
of from 10 to 15 per cent potassium dichromate in concentrated sulfuric 
acid. The liquid must be frequently stirred and the objects moved 
around one by one with forceps, in order to make sure that small air 
bubbles do not protect any part of their surface. As to graduates, test 
tubes, etc., the liquid at the bottom must be frequently changed by 
means of a glass tube with a rubber bulb attached by which the liquid 
is aspired. For the pipettes it is sufficient to adjust a rubber tube at 
one of the extremities and to produce by suction a rapid and frequent 
alternative movement of the liquid. The standard volumetric flasks must 
be filled with the cleaning solution which is kept at the boiling point for 
two hours, after which the liquid is allowed to cool for twelve hours, 
during which it should be shaken vigorously at least three or four times. 

The objects are then rinsed under a jet of distilled water. If the 
vessel containing the distilled water be of glass it must naturally have 
been subjected to the same process. The rinsing by running distilled 
water must be thorough. The different pieces are then allowed to dry 
in a place where they are protected from dust, in an incubator, for 
example, on clean filter paper. 



30 SURFACE EQUILIBRIA 

Under such conditions the .glass is clean. Nevertheless its "wetability" 
is not always perfect. As a rule it will wet if employed immediately 
after this treatment, but watch glasses which will wet uniformly on 
the first day often act like greasy glass after three or four days. This 
phenomenon is not well understood, but Professor Devaux, who has 
made a remarkable study of the "wetability" of surfaces, 16 has sug- 
gested a very simple and absolutely efficacious method to correct this 
fault. Flame the glass for a second or two over a Bunsen burner, 
taking care that the surface destined to be wetted is in contact with the 
flame. After cooling, water adheres to the surface in an absolutely 
perfect manner, a condition particularly essential when watch glasses are 
used to make measurements, for in certain of our experiments the free 
surface of the liquid must be known very exactly and this is only 
possible when it is perfectly circular. 

There is another reason why the wetability must be perfect. A 
platinum ring with a mean diameter of 12.73 mm. (circumference 
4 cm.) is used. For exact measurement it is necessary that the surface 
of the liquid may be considered as undeformed when the ring lifts a 
small mass of this liquid above its level. Theoretically, the measure- 
ments should be made in a vessel the diameter of which is large in 
comparison with the ring. This is easy to realise when considerable 
quantities of liquid are used. But in devising this instrument the aim 
was to obtain precise measurements with the least possible amount of 
liquid. The smallest possible limits for the dimensions of the vessel 
when a ring of 12.7 mm. diameter is used were determined experi- 
mentally. It was found that the minimum diameter was of from 5 to 8 
cm. when the liquid did not wet the glass, but only of 3.5 cm. when the 
wetability was perfect. Now in the watch glasses used by us, two cubic 
centimeters of water spread over a circle of from 4.1 to 4.4 cm. in 
diameter, which is more than is necessary. However, this is only true 
when the glass is thoroughly wet ; that is, if when using pure water the 
line of demarcation between the glass and the water is invisible. 

Preparation of the Solutions. 

The same care must be taken in the preparation of the solutions. 
For several months we were unable to obtain reproducible values for 
solutions of blood serum (rabbit) diluted to 1/10,000 in physiological 
salt solution (NaCl, 0.9 per cent). The figures of the initial surface 
tension varied from 63 dynes to 74 dynes (at about 20°). Appar- 

18 H. Devaux. Jnl. de Phys. 1923. IV, Ser. VI, p. 293. 



TECHNIQUE 31 

ently every precaution had been taken: the glassware was clean, the 
water was distilled twice in a clean still, the animals were identically 
bled after having been kept without food for the same length of 
time. Only one element had escaped our control: namely, the "chem- 
ically pure" sodium chloride which was delivered to us in bottles with 
ground glass stoppers. A concentrated filtered solution of this salt 
was prepared in a separating funnel and left to settle for twenty-four 
hours. The liquid was then decanted, leaving a large proportion in 
the funnel, the solution crystallised by evaporation and the crystals 
quickly washed in running hot water, so as to dissolve the surface of 
the crystal which might have been polluted by foreign substances con- 
tained in the initial solution. After drying in vacuo, a 0.9 per cent 
solution was prepared from these crystals and was used to dilute the 
serum of several animals at 1/10,000. All the measurements coincided 
within 0.1 dyne and since then tens of thousands of measurements have 
been made without a much larger discrepancy ever having been found 
in a single series of experiments. 

It is therefore necessary, when saline solutions are required, to dis- 
solve, filter and recrystallise the salts, taking care to protect them from 
the air. A concentrated solution is then prepared and kept in a sep- 
arating funnel with a ground stopper. This solution, collected through 
the lower tap or else by means of a rubber tube fitted with a pinchcock, 
is used to prepare the final solution. The advantage of this method 
consists in the fact that the organic impurities are adsorbed on the 
free surface and on the walls. By allowing a few cubic centimeters of 
the liquid to run off, one is almost certain to have only salt in the 
solution actually used. 

The water must be redistilled and kept in rigorously clean demijohns 
which are immediately plugged with lightly flamed corks. The less 
the water is transferred the fewer are the causes of error. In some 
of our experiments dilutions up to 1/50,000,000 had to be made. In 
such a case it is obvious that in order to make an experiment of any 
value, one must be reasonably certain that the solution does not contain 
the slightest trace of impurities, as 1/100,000,000 of organic matter 
might introduce an error of 50 per cent in the measurements. It must 
be admitted that these are extreme conditions but they should be con- 
sidered as normal if a relative constancy in the results is required. 

The solutions were prepared in the following manner : 
(Typical experiment with sodium oleate) 
Preparation of 44 solutions between 1/1000 and 1/2,000,000. 



32 SURFACE EQUILIBRIA 

1 gm. of anhydrous sodium oleate is weighed to the 4th decimal place 
on an analytical balance and poured into a 1,000 cc. standard volumetric 
flask. The glass used for the weighing is rinsed twice with redistilled 
water, the rinsing water carefully poured into the flask and about 
500 cc. of water added. It goes without saying that by "water" we 
always mean redistilled water kept in the manner described above. 
Dissolution of the sodium oleate is brought about by stirring gently 
so as to avoid the formation of foam. It is better to work in an 
atmosphere of nitrogen in order to avoid the fixation of C0 2 from 
the air. This is done by displacing the air by a rapid current of nitrogen 
introduced by means of a clean glass tube into the flask which is then 
instantly closed with its ground stopper. When the dissolution is 
completed, water at the temperature indicated on the standard, flask 
(20°), is added until the volume is 1,000 cc. It is important that the 
temperature of the liquid should be exactly 20°, and the thorough 
cleaning of the thermometer must not be overlooked as it might other- 
wise introduce a supplementary cause of error. 

This stock solution at 1/1000 is used for the preparation of the 
second stock solution at 1/100,000 and also of the intermediate solu- 
tions at 1/5000, 1/10,000 and 1/50,000. Let us call A the solution at 
1/1000, B the solution at 1/10,000 and C the solution at 1/100,000* 



1 cc. 
1 cc. 
1 cc. 
1 cc. 
or 

1 cc. 

2 cc. 
2 cc. 
1 cc. 
1 cc. 
etc. 


of sol. 

«« 11 
u u 
a it 

u a 
n u 

U M 

« u 

n n 


A + 4 cc. Water 
A + 9 cc. " 
B + 4 cc. " 
B + 9 cc. " 

A + 99 cc. " 
C + 2 cc. " 
C + 4 cc. " 
C + 3 cc. " 
C + 4 cc. " 


= 5 cc. at 1/5000 

= 10 cc. at 1/10,000 = sol. B. 10" 4 

= 5 cc. at 1/50,000 

= 10 cc. at 1/100,000 = sol. C. 10" 5 

= 100 cc. at 1/100,000 
= 4 cc. at 1/200,000 
= 6 cc. at 1/300,000 
= 4 cc. at 1/400,000 
= 5 cc. at 1/500,000 


1 cc. 

etc. 


of sol. 


C + 6.25 cc. water 


=7.25 cc. at 1/725,000 


y 2 cc 


. of sol 


. C + 9.5 cc. water 


= 10 cc. at 1/2,000,000 



It will be observed that the great majority of dilutions, between 
1/200,000 and 1/2,000,000, are prepared from the solution at 1/100,000. 

Before the solution at 1/100,000 is withdrawn in a pipette the flask 
must be agitated by a rotary motion, alternately clockwise and counter- 
clockwise for at least one minute, taking care to avoid the formation 
of bubbles, and the liquid aspired without stopping the rotation so 
as to obtain as homogeneous a sample as possible. It is unnecessary 

* This table is inserted owing to the number of inquiries the writer has 
received as to how the dilutions are made. 



TECHNIQUE 33 

to add that the pipettes used are of the so-called "Ostwald" type, stand- 
ardised at 20°. The final solutions may be made in test tubes of 
adequate size. Our test tubes had a mean capacity of 35 cc. and 
received a maximum of 10 cc. of solution. It is well to make frequent 
controls; for example, in the case cited above 39 dilutions were made 
from the solution at 1/100,000 and another sample was prepared from 
the solution at 1/10,000 so as to control one by the other. When 
preparing the dilutions the flasks should be agitated for several minutes. 
When a series of measurements is started, it is advisable in trans- 
ferring the solution to the watch glasses to begin with the highest 
dilutions, so that the same standardised pipette may be used for the 
whole series. The error thus introduced is less than if a clean pipette 
were used for each measurement. Unless otherwise stated, the meas- 
urements quoted in this work were all made in watch glasses 51 to 52 
mm. in diameter and with as constant a radius of curvature as possible.; 
(Spherometer reading, from — 7 to — 7.5.) The quantity of liquid 
employed was always 2 cc. and all the measurements were made be- 
tween temperature extremes 20° and 22°. During the course of a series 
of experiments the variations in temperature never reached 0.5°. The 
only standardised pipettes required are pipettes of 1, 2, and 5 cc. The 
platinum ring is flamed after each measurement. j 

Experimental Set-up. 

It is extremely important when measuring the drop of surface ten- 
sion as a function of time, or the static value, to protect the solution! 
from vibrations or shocks. The influence of a slight agitation on the 
readines will be shown in Chapter 2. We were therefore compelled to 
use a special set-up of which an idea can be had from Plate I. 

Instead of the tensiometer being kept stationary and the solutions 
manipulated, the tensiometer is placed on a small carriage, rolling on 
two steel rails and brought successively in front of 44 watch glasses 
placed at the proper height on a rigid platform. The superior part of 
the tensiometer, comprising the torsion wire, the arm and the vernier, 
glides in the base and can be raised or lowered by means of a rack and 
pinion. The contact between the platinum ring and the liquid is there- 
fore obtained in this manner and not, as in the case of isolated meas- 
urements, by the raising of the table of the instrument. A metallic 
hood bent at right angles over the solutions protects them from the 
agitation of the air and from dust. The glasses are placed in holes 
bored in the platform. The whole is bolted on a long table of con- 



34 



SURFACE EQUILIBRIA 



venient height, the legs of which rest on concrete columns which pass 
through the floor to avoid the vibrations due to the steps of the experi- 
menter. The dimensions of these tables depend on the available space. 
Three tables, each carrying 44 watch glasses, can be easily placed in a 




Plate I. — Apparatus for measuring the static value of .the surface tension of 
series of solutions. The tensiometer is seen rolling on rails in front of the 
watch glasses containing the solutions on a rigid table protected against 
vibrations. 



room 15 by 18 feet. Each table is equipped with a gas connection 
feeding two Bunsen burners for flaming the ring. Counting the two 
hours which elapse between the initial measurements and the static 
measurements, about four hundred determinations per day could there- 
fore be made. 



Chapter 2. 

Drop of the Surface Tension of Colloidal Solutions 
as a Function of Time. 

When, in studying the surface tension of any colloidal solution with 
the preceding technique, measurements of the solution in a watch glass 
are taken every two minutes, for instance, it is found that the value 
of the tension decreases regularly. At the end of two hours it appears 
fairly constant in most cases ; but if another measurement be taken 
after twelve or twenty-four hours, it is generally observed that another 
decrease has taken place, although of a much smaller magnitude than 
the first. This is the fundamental fact on which all the following work 
is based. Some colloidal salts and colloidal oxides, however, such as 
arsenious sulphide, ferric hydroxide and manganese dioxide, did not 
show any drop. 

After a certain length of time depending on the conditions of the 
experiment, a stable value is attained. This is the static value of the 
surface tension. Table II gives these values for a few dyes. The 
classification followed was that of Taylor. 1 It will be observed that 
their behaviour with respect to surface tension is similar although some 
are classed as crystalloids. 

The phenomenon can be followed qualitatively but not quantitatively 
when the afore-mentioned technique is used (measurements of the 
surface tension of the same solution, repeated at intervals), on account 
of certain causes of error inherent in this method. It is obvious that 
every measurement, every tearing off of the film, brings about a disturb- 
ance in the surface. Supposing it is desired to follow the phenomenon 
every two minutes, the 10th measurement, for example, taken after 
twenty minutes, will not in any way correspond to a measurement made 
in a solution left to settle for twenty minutes. The ten successive stir- 
rings will certainly have retarded the establishment of the equilibrium 
and the phenomenon Will appear much slower. Furthermore, a certain 

*W. W. Taylor. The Chemistry of Colloids, Longmans, Green. N. Y. 
19115, p. 270, 271. 

35 



36 



SURFACE EQUILIBRIA 



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DROP OF THE SURFACE TENSION 



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DROP OF THE SURFACE TENSION 39 

mass of the liquid which is supported by the film, the tension of which 
is to be measured, is raised when a measurement is made. This mass 
assumes outwardly the shape of a surface of revolution. This rela- 
tively rapid deformation of the surface is, perhaps, of a nature to 
modify the molecular structure of the surface, and as the measurement 
follows immediately after, there is no time for the equilibrium to be 
reestablished. A third cause of error is the personal coefficient of the 
experimenter. How can it be affirmed that the speed with which the 
ring has been raised and the time which has elapsed between the contact 
of the ring with the liquid and the rupture, are constant in all the 
experiments ? 

These three principal causes of error induced Us to establish a method 
from which they would be completely eliminated. 2 

This is done by preparing the same number of watch glasses, or Petri 
dishes, as it is desired to establish points on the curve ; that is, as many 
as there are measurements to be made, let us say ten, for example, all, 
of course, as identical as possible. A certain quantity of liquid (2 cc. 
in the case of watch glasses) is poured into the first glass which is 
already placed on the table of the tensiometer. The solution is stirred 
up to the last second and the measurement made very rapidly. To lose 
as little time as possible in making the measurement it is advisable, 
while turning the torsion wire (vernier at 40 dynes, for example, for 
a solution of which the surface tension is of the order of 60 dynes), 
to agitate the liquid with the ring itself. If the film does not break the 
torsion is then increased and the stirring renewed. If the tension of the 
wire is still too weak to break the film, it is increased again and the same 
procedure is repeated until the rupture is produced. Thus the reading is 
made less than a second after the agitation in the watch glass has 
ceased. This reading is the highest that can be obtained ; let us call it a. 
Then the second glass is filled and placed on the table. The ring is 
immersed and the torsion of the wire increased just as if a measurement 
were to be taken. But instead of raising the vernier to the value of the 
preceding rupture a, it is set at a value which is lower by 1 dyne (or 
a fraction of a dyne) e.g. a — 1. The liquid is thus raised and deformed, 
but the rupture does not occur. It will only take place when the surface 
tension will have decreased by one dyne, or, more exactly, by one dyne 
plus a small fraction (less than 0.05 dyne), for otherwise there would 
be equilibrium and no rupture. The time which has elapsed can be 
3 Lecomte du Noiiy. J. Exp. Med. 1925, XLI, p. 663. 



40 



SURFACE EQUILIBRIA 



measured by a stop-watch or, better still, automatically recorded by 
the instrument itself on the smoked drum of a kymograph, by means 
of an electric contact established at the moment of the rupture (see 
Fig. 2) . This glass is again eliminated, a third one filled, and the process 
repeated and the vernier stopped at the value a — 2 dynes. The time 
which will elapse before the rupture will obviously become longer and 




Tensiometer No.l 



Tl®«t 




Fig. 2. — Set-up of the electrical connection of the tensiometer to the kymograph. 
The current provided by the two dry cells E passes through the tensiometer 
and the torsion wire. When the film breaks, the lever is released, and the 
end a of the clamp A hits against the wire b. This establishes the electric 
contact which energizes the magnetic recorder and leaves a mark on the 
drum. T is the time recorder. K is the kymograph. B supports the wire b. 



longer, for the rapidity with which the surface tension diminishes gradu- 
ally decreases as the molecules or micellae are adsorbed in the surface 
layer. 

The points of the curve are obtained in this manner. The values of 
surface tension are plotted as ordinates and the time as abscissae. The 
three causes of error pointed out above are clearly eliminated. This 
method allowed us to study the phenomenon from its very start with 



DROP OF THE SURFACE TENSION 



41 



the greatest possible precision. Figures 3, 4 and 5 express some of 
the results obtained with blood serum and sodium oleate. 

The mechanism of the phenomenon can thus be understood, as well 
as the reason why it is dangerous to mention the value of the surface 
tension of any colloidal solution without also giving the time that has 
elapsed from the moment when, as the result of a violent agitation, 
the solution can be considered as homogeneous with respect to the 



Dynes 


Nopmdl p&fcbit sepum 


NO. 1 




































•76 
75 
74 
73 
72 
71 




N 


\ 


* 








































\ 
















B \ 






\ 






























































\ 








1/20,000 




3r 67 

« 66 












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65 

64 


























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B 
















i/iu,uuu 




63 
62 
61 
60 
59 






























A \ \ 
















tAfloo 


































. 


























1/100 . 





Min.0 



75 
Time 



120 



150 



Fig. 3. — Decrease in the surface tension of serum as a function of the time. 
Note the delay in the drop at 1/20,000 which can be observed at 1/10,000, 
although to a lesser degree. 



distribution of particles or molecules, to that when it ceases to be so, 
owing to the adsorption of the molecules in the surface layer. This 
point is extremely important, for a surface tension, measurement has 
no significance unless it applies either to a homogeneous system, as 
defined above, or to a system having attained a state of equilibrium. 
Most of the values so far published correspond to an unstable state in 
course of evolution towards the equilibrium and only happen to give 
approximately constant values when the instruments used (in the case 



42 



SURFACE EQUILIBRIA 



of hanging drop methods) are identical and when the time required 
for the formation of a drop and its fall is about the same. The con- 
cordance of the figures does not in any way imply the identity of the 
values of the tensions, except when, all things being otherwise equal, 
the time required in the formation of each drop is the same for a large 



rynes 
76 
75 
74 



73 



71 
70 
69 

c 68 
8 67 

ti 66 

!« 

63 
62 
61 
60 
99 
56 
57 



Nopm&l rabbit serum No. I 





















\\ 


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o ~ - 




























1/100 





































































Kin. 



30 



«a 



60 75 

Time 



90 



105 



120 



li5 



Fig. 4. — Decrease in the surface tension of serum solutions as a function of the 
time. In this case also the delay in the drop at 1/10,000 can be observed, 
although it is not as marked as at 1/20,000. 



number of drops. As an illustration, let us consider Figure 4. One of 
the curves expresses the decrease of the surface tension of a solution of 
serum at 1/100. In the first minute the drop in the surface tension is 
about 2.5 dynes. According to whether a drop is formed in 10, 30 or 
60 seconds, the value of the surface tension calculated from the drop 
weight will be somewhere on the curve between 66.5 dynes and 64.0 



DROP OF THE SURFACE TENSION 



43 



dynes. This automatically eliminates all drop weight methods in the 
case of colloidal solutions. 

The rapidity with which the molecules are adsorbed in the surface 
layer in the beginning is considerable. In a solution of sodium oleate 
diluted to 1/25,000, for example, the drop is equal to 26 dynes in one 
minute, as illustrated by Figure 5. In this case, the rate of decrease for 
the first minute being proportional to the time, it can be said that the 
surface tension decreases at the rate of 0.43 dynes per second, from 68 



W 65 

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32 dynes 


e at 




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"T7me>i 2 3 4 3 



10 

Fig. 5. 



20-Min. 



dynes down. But this in no way signifies that above this value it has 
not decreased with a much greater rapidity and dropped from 71 dynes 
to 68 dynes in less than one- tenth of a second ; in fact we are incapable 
of measuring the surface tension of this solution instantaneously, be- 
fore any adsorption has taken place. The adsorption begins as soon 
as the solution is no longer violently stirred. During the first hun- 
dredth of a second, the drop may be of the order of magnitude of 1 
dyne or more, and greater still in the first thousandth of a second. 

This observation led us to try to obtain an idea of this rate which 
certain authors have estimated to be of the order of magnitude of 



44 



SURFACE EQUILIBRIA 



10~ 5 seconds. Solutions of blood serum were used because of their 
stability and because of the size of their protein molecules which are 
less rapidly adsorbed. The rate of adsorption expressed by the recip- 

















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Concent p cd ion 



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Fig. 6. — Rate of decrease of the surface tension expressed as 



1 



plotted 



tg. A 

against concentration, on logarithmic paper. The dotted curve is extrapo- 
lated. 



rocal of the tangent of the angle of the tangent to the curve with the 

axis of ordinates, — j, was plotted on logarithmic paper as ordinates 
tgA 

against the concentration (Fig. 6). It will be seen that the curve which 

results shows a very clear break at a concentration of 1/10,000. (Later 

on it will be shown that this sudden change of direction is due to the 

fact that it corresponds to a monomolecular layer, and that in the lower 



DROP OF THE SURFACE TENSION 45 

concentrations the number of molecules is insufficient to cover the sur- 
face of the liquid, while in the higher concentrations, under 1/10,000, 
there is an excess.) We are not concerned with the straight line ex- 
pressing the rate at high concentrations, for the concentration is such 
that the surface tension drops almost instantaneously from the value 
of water to that actually measured. To analyse the phenomenon it 
is necessary, on the contrary, to study the low concentrations, in which 
case the surface tension can be measured from the moment when the 
tension is about equal to that of water. Under such conditions, the 
rate of adsorption during the first second is measured and an extra- 
polation up to the high concentrations can be attempted. 

It will be seen in Figure 6 that the curve appears regular for the con- 
centrations below 1/10,000. If we express the rate of adsorption as a 
function of the time required to lower the tension by 1 dyne, we shall 
find 1 dyne per minute for the concentration at 1/10,000 and 1 dyne 
in 7y 2 minutes for the concentration at 1/20,000. By extrapolating 
the curve up to the concentration at 1/1,000 a drop of 1 dyne in 5 X 
10 -5 seconds, or 1/50,000 of a second, is obtained. Though this 
figure is of the same order of magnitude as those estimated by certain 
authorities, it should only be taken as an indication with a certain 
amount of probability but without real experimental foundation. 

Nevertheless the preceding facts explain why it is necessary to resort 
to the high dilutions, if it be desired to follow the phenomenon from 
the beginning up to the establishment of the equilibrium. As the 
adsorption in the case of concentrated solutions is so rapid that in 
one hundredth of a second the surface tension is materially decreased, 
this method does not allow the study of the phenomenon from the start. 
By concentrated, we mean solutions up to approximately 1/10,000 in 
the case of serum and up to 1/100,000 in the case of sodium oleate. 
It must be borne in mind that a dilution of 1/10,000 of serum corre- 
sponds to a concentration of the proteins of about 1/166,000 (rabbit 
serum). What is then usually considered as the dynamic or initial 
surface tension is nothing but an arbitrary value, which depends on the 
rapidity with which the measurement can be made and which is the 
further removed from the real value of the initial tension the longer 
the time required for the measurement. 

These curves also show that the static tension is not proportional to 
the concentration. Another phenomenon comes into play: the organ- 
isation of the molecules and their orientation. This will be studied 
separately. 



46 SURFACE EQUILIBRIA 

When concentrations around 1/10,000 are used for serum, it is found 
that the initial tension is ahout that of pure water. A few minutes 
later the tension is already lowered and its fall will continue regularly 
following a logarithmic law. This law cannot easily be expressed by 
a simple equation, for the curve becomes a straight line at high dilutions, 
at 1/20,000 for serum, and at 1/100,000 for sodium oleate, for example. 
The surface tension of water cannot begin to decrease until the surface 
layer is invaded by a sufficient number of molecules. The tension does 
not change as long as the number of adsorbed molecules is so small 
that there is a certain distance between them. This delay in the begin- 
ning of the phenomenon can be observed at 1/10,000 for serum but is 
much more marked at 1/20,000. Thirty minutes elapsed in the latter 
case before a slight decrease in the surface tension of water could be 
observed, as illustrated by Figure 3. The fall is of 3 dynes in the 
fifteen minutes that follow and the rate of the fall then remains nearly 
constant until equilibrium is attained. 

The existence of a monomolecular layer will be studied in Chapter 3, 
although it was necessary for the sake of clearness to mention it in 
this chapter. 

It has been stated that, in the case of rabbit serum, this layer was 
produced around 1/10,000. At 1/20,000 the number of molecules 
is decreased by one-half and the formation of such a layer, which, in 
any event, could only exist when the equilibrium was attained, is there- 
fore impossible. It must then be admitted that in the case of sub- 
stances in solution, the surface tension of the solvent begins to decrease 
long before a monomolecular layer is formed. This is in accord with 
some of Langmuir's observations 3 on monomolecular layers of non- 
soluble substances on water. Langmuir states that the surface tension 
of water remains constant as long as the monomolecular layer of certain 
substances (higher fatty acids) is not complete, when a sudden fall 
takes place. The lower fatty acids, however, behave in a manner similar 
to that of the colloidal solutions and the decrease takes place before 
the completion of the monomolecular layer. 

These phenomena are always observed in the case of colloids and the 
general aspect of the curves is the same in all cases. It is difficult, how- 
ever, to reproduce two experiments quantitatively when dealing with 
serum from another animal or with different lots of C. P. sodium oleate. 
The ratio between the angles A lf A 2 , A 3 (Fig. 5) is generally the same, 
but the absolute values of the angles vary. It is interesting to note that 

3 Irving Langmuir, J. Am. Chem. Soc. XXXIX, p. 1888. 



DROP OF THE SURFACE TENSION 47 

each of these angles is very nearly three times as large as the preceding 
one. The reciprocals of the tangents of these angles express the rate 
with which the surface tension decreases. These tangents are : * 

^.^3 = 0.613 corresponding to a concentration at 1/100,000 
tg.A 2 = 0.185 " " " " " 1/50,000 

tg.A 1 = 0.066 " " " " " 1/25,000 

The ratio between the successive tangents is nearly 3, whilst the ratio 

between the concentrations is 2. An important part is played in this 

, , , t P , surface of adsorption . . .„ , 

phenomenon by the value ot the ratio : r— : — t-. — r-r- I this will be 

volume of the liquid 

further discussed in Chapter 3. 

When the equilibrium value is attained it remains constant. No 

rupture occurs in two hours if the torsion of the wire exerts a force 

inferior by 0.1 dyne to this value. 

Action of Stirring. 

If the solution be stirred, or even slightly shaken, after the static 
value is reached, the surface tension rises immediately and can attain 
its initial value. This was to be expected, as the decrease in surface 
tension is due to the adsorption of the molecules in the surface layer, 
and as the stirring brings back the system to its original and more or 
less homogeneous state. Figures 7, 8, 9 illustrate this phenomenon in 
the case of pure blood serum. Figure 8, in particular, shows the pro- 
gressive decrease in the rate of adsorption. By expressing the phe- 
nomenon by the formula : 4 

Y = y e~ kt 
which corresponds to the facts in a certain number of cases, one finds 
for the coefficients K in the experiment in question (Fig. 8) the suc- 
cessive values: ^ = 0.01 (1st drop), K 2 = 0.005 (2nd drop) and 
iv" 3 = 0.0032 (3rd drop). 

The above formula, though only approximate, makes it possible in 
some cases to obtain curves in good agreement with the experiment, 
as in the example just mentioned. It is better adapted to the phenomena 
that we are studying than the formula suggested by Freundlich. 5 How- 
ever, too much importance should not be attached to it, as it is far from 
being applicable to all cases. Nevertheless, by replacing t (time) by c 

* Lecomte du Nouy, J. de Phys., 1925, VI, Ser. VI, p. 145. 
4 Lecomte du Nouy, J. Exp. Med., 1922, XXXV, p. 591. 
5 H. Freundlich, Kapillarchemie, Leipzig, 1909, p. 146. 



48 



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2 4 6 8 10 2 4 6 8 10 min 

2 4 6 8 10 10 20mm. 



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20 



35 min. 
2 4 6-35 min. 



(concentration), it is possible to express with satisfying accuracy a 
phenomenon studied by McC. Lewis, 6 i.e. the adsorption of sodium 
glycocholate by paraffin oil (Figs. 10, 11). 

Dynes 

1 59 

a 58 

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5 15 25 35 45 55min 

.10 20 30 40 50 60 70 mm 



Fig. 9, a to e. — (a to d) Effect of stirring on the surface tension of serum. 
(e) Behaviour of a control sample of the same serum, left unstirred during 
the 2 days, and stirred on Oct. 23, at 4 p.m., for the first time (precipitate at 
the bottom). Original value on Oct. 21, 56.5 dynes. 



Figure 9 represents an experiment with serum extending over three 
days; it is thus possible to follow the complete evolution of the phe- 
nomenon. It shows that the presence of an insoluble precipitate pro- 
duces after stirring a rise in the value of surface tension. It also shows 

e W. C. McC. Lewis. Proc. Phys. Soc. 1909, XXI, p. 150. Phil. Mag. 
1909, XVII, p. 466. 



50 



SURFACE EQUILIBRIA 



that before the production of these insoluble substances, the magnitude 
of the phenomenon tends to decrease. The first stirring, after ten 
minutes, brings the surface tension back to its initial value (increase 



Dynes 

34 



30 



26 



22 



13 






0.1 



0.2 



0.3 0.4 

Concentration 



0.5 



06 



Fig. 10. — Action on surface tension of adsorption of sodium glycocholate by 
paraffin oil (McC. Lewis; adsorption isotherm). 



This result can be 



2 dynes). The fourteenth stirring only produces an increase of 0.5 
dyne and the sixteenth is without result (after two days). 7 The serum 
appears to have reached a state of equilibrium. 

Dynes 
y 59.5 



59.0 



58.0 



57.0 



56.0 
Time 12 3 4 5 6 7 8min. 

Fig. 11. — Action on surface tension of adsorption in the surface layer of serum. 

explained by admitting that pure serum left to itself undergoes a modifi- 
cation which is manifested by a progressive decrease of the solubility 
of certain of its constituents. At the beginning of the experiment the 
T Proper precautions were taken to prevent infection. 



TO: 



DROP OF THE SURFACE TENSION 



51 



protein molecules are free ; a certain number of them are agglomerated 
in the form of micellae, but the solution is still mainly a true solution 
in the chemical sense of the word. The accumulation of the molecules 
in the free surface of the liquid produces the decrease in the surface 
tension. Stirring reestablishes the homogeneity and the phenomenon 
begins all over again. But time intervenes, and the molecules under 
these new conditions begin to lose their individuality, and agglomerate 

Dynes 



74 




































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68min. 



Fig. 12.— Effect of stirring on solutions of serum. Dilution 1 : 10,000 dog serum. 
The dotted line is calculated according to the formula y = y <?-/£'*. 

as micellae. The micellae cannot exert the same action on the surface 
tension of the solvent as the isolated molecules, for they have lost their 
polarity. Each successive stirring, therefore, liberates a decreasing 
number of active molecules in the solution and consequently the phe- 
nomenon of the drop and reestablishment must show an ever smaller 
amplitude tending toward 0. The figure d (Fig. 9) shows that precipi- 
tation may occur and that the stirring of the precipitate causes the 
tension to reach a value higher than its initial value, of 60.5 dynes. 



52 



SURFACE EQUILIBRIA 



This is usually found to be the case. Figure 12 illustrates the effect of 
stirring on a dilute solution of serum. 

TABLE III. 
Time Drop of Metallic Colloids, Electrically Prepared. 





Dynamic or 
Initial Value 


Static Value 

(2 hours 

standing) 


Difference 


Gold 


72.5 dynes 
72.5 " 
75.0 " 


65.5 dynes 
63.5 " 
66.5 " 


7.0 dynes 
9.0 


Silver 


Aluminum 


8.5 







Similar Solutions, Heated at 100° for 5 Minutes ani 
Room Temperature. 


Cooled to 


Gold 


75.3 dynes 
65.5 " 
68.5 " 


62.0 dynes 

57.2 " 
59.5 " 


13.3 dynes 
8.3 " 


Silver 


Aluminum 


9.0 " 







An examination of Table III will show that the drop in the surface 
tension of colloidal solutions of metals is somewhat smaller than that of 
certain organic colloids at high dilutions. This is probably because the 
colloidal micellae of metals are so shaped that they cannot organise them- 
selves as perfectly as the organic molecules. Furthermore, their 
concentration is always very low. The organic molecules form a real 
film, semi-solid and sometimes even solid. The existence of such films 
had already been observed in 1904 by Ramsden. 6 We were able quite 
recently to measure the rigidity of these membranes and to show that 
the surface viscosity of organic solutions increases considerably as a 
function of time. 7 As the phenomenon of adsorption runs parallel to 
the decrease of surface tension, it can thus be followed in two different 
ways (see Chapter 7). 

Action of Heat on the Surface Tension of Serum. 

The dynamic and the static surface tension of rabbit serum kept 
at different temperatures were studied in the following way : each 
sample of serum taken from one normal animal was divided into three 
lots. The first lot was kept in the ice-box at a temperature near 0° ; 
the second at room temperature near 22° ; the third in a thermostat at 
55°. The vessels containing the sera were stoppered to prevent evapo- 
ration. Before the measurements, the sample kept in the ice-box and 

9 W. Ramsden, Proc. Roy. Soc. London, 1904, XXII, p. 156. 
7 Lecomte du Noiiy, Science, 1925, LXI, p. 117. 



DROP OF THE SURFACE TENSION 



53 



the one in the thermostat were removed and kept in the laboratory 
until their temperature reached that of the second sample. Then 2 cc. 
of the liquid were removed from each vessel and poured into the watch 
glasses where the measurements were made. The results of a series 
of five experiments made with different sera are expressed in Table IV 




Houps 



Time 

Fig. 13. 



and Figures 13 to 16. Figure 13 gives the values of the initial surface 
tensions (dynamic) of serum kept at 55°, over a period of seven days. 
The results expressed as mean curves will be found in Figures 14 and 
15. It is apparent that heat at 55° decreases the value of both the 
dynamic and the static surface tensions, but especially that of the 



s 

54 



52 



Hours 





Initial values (-mean of 5 exp} 






— *--~jsrzszi 


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46 



72 



96 



166 



Time 

Fig. 14. 



dynamic surface tension. The time drop is decreased in all cases on 
the 4th and on the 7th day (Figure 16 and Table IV), but is completely 
annulled only in the case of the heated serum, after 168 hours, in which 
case the difference, 0.1 dyne, is of the order of magnitude of the experi- 
mental errors. 

The temperature coefficient of the serum is greater than that of pure 



54 



SURFACE EQUILIBRIA 





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pee- 



DROP OF THE SURFACE TENSION 



55 



water. (Fig. 17.) This was found to be the case for a number of 
colloidal solutions and confirms the observations of Bernstein. 8 

As might have been forecast, a physico-chemical transformation un- 
doubtedly occurs in the serum heated at 55°. It is known that a bio- 



















i J0 








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52 












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2 


4 


46 72 
Time 


96 




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Fig. 15. 



logical manifestation of this transformation is the destruction of the so- 
called "complement." But this phenomenon is not chemically defined. 
This modification, which until now had not been demonstrated by any 
physical or chemical methods, also changes the appearance of the NaCl 




2 3 

Time 
Fig. 16. — Action of temperature on the time-drop of serum. Mean values. 



crystals when the serum is diluted to 1/10. Plates II, III, IV, V, VI 
illustrate this fact. Our knowledge of the chemistry of proteins does 
not yet permit us to draw any conclusions as to its interpretation. 

Figure 18 expresses the results obtained in studying the time drop 

8 J. Bernstein. Pfluger Arch, fur Physiol. 1908. CXXII. pp. 129-191. 



56 



SURFACE EQUILIBRIA 



76 
T4 
72 
70 
68 
























^ 








Rabbit se-pum *54 






"~- 


^e» 












































































g 66 

I 62 

M 60 


^ 




>. 


















L 




















% 


H 


































X 




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Kt- 






















<^e 














52 
50 
4ft 




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? 










































\47.6 


d. 













Temperature 
Fig. 17. — Temperature coefficient of pure serum. 

of heated solutions of serum. Usually it seems that heating above 55° 
is followed by a marked decrease of the static value of surface tension, 
especially at the critical concentration of 1/10,000 which corresponds, 
as will be seen later, to the existence of a monomolecular layer. It is 
surprising to observe that in this case the minimum is not shifted, 



16 



14 
CO 

c 10 



o 

1 



8 



H 4 













Aioo 










































^5 


sVft 




















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100° 


















Vr^ 


A 


70° 




















•56° 
•25° 



10 



10 



-z 



10" 3 io- 4 
Concentration 



10' 



10" 



Fig. 18.— Time-drop in 2 hours, as a function of the concentration, at different 
temperatures (Rabbit serum). 



DROP OF THE SURFACE TENSION 



57 




Fig. 1. 



Fig. 2. 




Fig. 3. 



Fig. 4. 



EXPLANATION OF PLATE II. 

Figs. 1 to 4. — Action of temperature on the crystallisation of serum solutions, 
concentration 1/10 in saline solution 0.9 per cent (rabbit serum). 

Fig. 1. Unheated. 

Fig. 2. Heated at 56° C. for 2 hours. 

Fig. 3. Heated at 70° C. for 1 hour. 

Fig. 4. Heated at 100° C. for 5 minutes. 



58 



SURFACE EQUILIBRIA 




Plate III. — Photomicrograph of 1 drop of serum diluted to 1 : 10 in saline 
solution. Kept at room temperature. X 20. 



DROP OF THE SURFACE TENSION 



59 















- 










Plate IV. — Photomicrograph of 1 drop of serum diluted to 1 : 10 in saline 
solution. Kept at 55° C. for 2 hours. X 20. 



60 



SURFACE EQUILIBRIA 



. < 






.;*•■ 



i. 



. < 












.-'»»J 






-<ft 
















>'^& 



l^fex 



/ 



Plate V. — Photomicrograph of 1 drop of serum diluted to 1 : 10 in saline 
solution. Kept at 70° C. for 1 hour. X 20. 



DROP OF THE SURFACE TENSION 



61 




Plate VI.— Photomicrograph of 1 drop of serum diluted to 1 : 10 in saline 
solution. Kept at 100° C. for 5 minutes. X 20. 



62 



SURFACE EQUILIBRIA 



which indicates that everything happens as though the dimensions of 
the molecules were not changed. 9 

Influence of Gases. 

For the study of the action of C0 2 , N 2 and 2 on the surface tension 
of solutions, the watch glasses containing the latter were simply covered 
by a small inverted glass funnel into which the gases were allowed to 
flow through a rubber tube after bubbling through water. The flow 




Plate VII. — Setting for the study of the action of gases. 



was so regulated as not to accelerate the evaporation of the liquid, which, 
in the open room, required normally about 24 hours. By a slow current 
of moist gas this rate could be retarded to about six or seven days. 
Under these conditions 2 cc. of solution evaporated at speeds which 
differed according to the rate of the gas current and according to 
whether the gas had been more or less completely dried after' washing 
with water. (Plate VII.) 

When evaporation was completed, 2 cc. of distilled water were poured 
into the watch glasses and stirred until the dried substances were com- 
pletely dissolved. The surface tension was measured immediately after 

9 Lecomte du Noiiy, J. Exp. Med., 1922, XXXVI, p. 547. 



DROP OF THE SURFACE TENSION 



63 











irs-A\ 






















Initial value 










i 


































( 


1 ( 




„.< 


- c 


J2_:frpa. 








*" i"" 







p T6 

P 

£ 72 
70 

68' 

66 

Fresh 1 st 
solution 



2 nd 



3Pd 4 th 
Drying 



6 th 



rth 



Fig. 19. — Surface tension of serum dried and redissolved in water. 



76 

74 

. 72 

I™ 

C 65 
?*> 

P 66 
64 
62 
60 



CO 2 atmosphere (Dilution 10" 4 ) 












mixta 


l veaue 


































> 














\ 






>. 


2 hrs. 






\ 






*■-< 


>-'' 






\ 




/' 







































Fresh 1 st 
solution 



2^ o 1 ^ 4 th 5* h 6 th 
Drying 

Fig. 20. 





"KMtt> 


nKn-r^ 




















76 « 








Initial value 
















I 72 

^70 

Q c 
66] 








































2 lYPS 






66 


\ 












64 
62 


\ 






c 












/ 










60 


\ 


f 











Fi?esh 
solution 



3 rd 4 th 5 th 6 th 
Drying 

Fig. 21. 



,ih 



64 



SURFACE EQUILIBRIA 



the stirring and again two hours later. This procedure was repeated 
several times. Figures 19, 20, 21 express the results obtained with 
different gases on serum diluted at 1/10,000. 

It is to be noted that if at the end of the second evaporation an in- 
crease in the drop is generally observed, this increase does not persist 
and at the end of seven successive dryings the drop is the same as on 
the first day. 

Critical Concentrations. 

It seems logical to suppose that the magnitude of the drop of the 
surface tension would diminish as the solutions are more diluted. This, 
however, is not the case. The static value of surface tension not being a 
simple function of concentration, as we have already pointed out, re- 



§- 



15 
14 
13 
12 
11 
10 

9 

8 

7 

6 

5< 

4 

3 




























































\ 




































\ 






































\ 




































\ 


L 




































\ 




































\ 






































\ 




































\ 































































































































































































10' 



io- 



io-* 

Concentration 



Fig. 22.— Drop in the surface tension of serum solutions in 2 hours. 
Rabbit serum. 



mains nearly constant within a certain range, and only begins to increase 
with the dilution when a definite value is attained. The initial or 
dynamic surface tension, on the other hand, increases regularly as the 
concentration decreases, up to the value of the surface tension of the 
pure solvent. The result is that the drop of surface tension, or the 
difference between the two values, increases with the dilution up to a 
certain point (Fig. 22). 



DROP OF THE SURFACE TENSION 



65 



It is easy to understand why the initial tension increases when the 
quantity of surface-active substance decreases, but it is harder to admit 
that under the same conditions the static tension remains nearly con- 



Dynes 
75 

70 

65 

60 

55 



















Initial 
> value 




















^<<? 


After 
->lhr. 

Aftrp 


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+'l 


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1 


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10" 



10" 



10" 4 10" 5 10" 
Concentration 



Fig. 23. — Values of the surface tension of serum solutions as a function of the 

time. Rabbit serum. 

stant or even, in certain cases, decreases. Yet this is what actually 
happens when blood serum, for instance, is used (Figs. 23, 24). The 
drop in surface tension increases up to the 1/10,000 dilution, then de- 
creases and eventually disappears entirely at the very high dilutions 



Dynes 
75 

70 

65 

60 

55 

















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le 
















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Zhps 





fcl 










^ 








I 




"*•*.„. 






^ 













10 



-2 



10 



10" 4 10" 5 10' 6 
Concentration 



Fig. 24. 



-Values of the surface tension of serum solutions as a function of the 
time. Rabbit serum. 



around 1/1,000,000. Now the increase in the value of the drop is due 
to the fact mentioned above, i.e. that the dynamic value increases when 
the static value remains constant; and the decrease in the value of the 



66 



SURFACE EQUILIBRIA 



drop is due to the exactly opposite fact, i.e. that the static value in- 
creases when the dynamic value remains constant (see Figure 29). The 
difference between the two values, which we term time-drop, thus at- 
tains a maximum. Figure 25 shows that this maximum occurs at 
different concentrations for different substances. In this figure the 
time-drop in two hours was plotted against the concentration. 




Concentration 

Fig. 25. — Drop in the surface tension of different solutions as expressed by the 
formula 

— dy = Yo-Y 



When solutions of different substances (oleate, taurocholate, gly- 
cocholate of sodium, saponin, hemoglobin, etc.) contain a small quan- 
tity (1%) of sodium chloride, the drop of the surface tension in two 
hours is greater. This phenomenon is also produced with other salts 
and was mentioned by us in 1922. 9 It was recently taken up again by 
Seith, 10 who has made a very thorough and interesting study of the 

9 Lecomte du Noiiy, J. Exp. Med. 1922, XXXV, p. 707 and XXXVI, p. 547. 

10 Wolfgang Seith, Z. Phys. Chem. 1925, CXVIII, p. 257. 



DROP OF THE SURFACE TENSION 



67 



subject. We reproduce here three figures from our own articles, deal- 
ing with blood serum and glycocholate of sodium (Figs. 26, 27, 28). 

The phenomenon of the drop can be expressed as a function of the 
concentration as shown in Figure 29. After the generality of this fact 



bO 






. fi& 




75 
70 
65 

C 55 
ft 50 

45 
40 
35 
30 


| 


Sodium ole&te 




**&"& 


Oy/ 












J?/ 


> ?/ / cy 




/ 








Alnit 


{&x / / 


7 /<$ 






/ /Static 


/ 




/ i 


/ /2h.^-" 




/ ^ 


y/,^ 




I i 


J2& 


s' _^-c^--< 


"*' 




to-* J 


ff 


1( 


j-4 J 


r 5 10" 



CcncentT'Ation 

Fig. 26. — Action of salts on the surface tension of sodium oleate solutions at 
different concentrations. (NaCl, 1 per cent.) 

had been established in the case of serum, the question arose whether 
the point which corresponds to the maximum of the drop (around 
1/10,000) and which is followed almost immediately by a sudden 
increase in the surface tension, did not correspond to a special state 
of the adsorbed layer. To elucidate this point, a series of dilutions 




Concent'pa.tio'n 

Fig. 27.— Action of NaCl on the time-drop of sodium oleate (NaCl, 1 per cent) 

between 1/8,000 and 1/12,500 were prepared and the measurements 
made in standardised watch glasses according to the technique described 
in the preceding chapter. The results of three successive experiments 
are given in Table V. The experiments were repeated with the same 



68 



SURFACE EQUILIBRIA 



sera five and ten days later, so as to ascertain whether a shift had 
taken place. The results were identical. These three particular sera 
showed in each case an absolute minimum of their static surface tension 




10* 

Concentration 

Fig. 28.— Action of NaCl (1 per cent) on the time-drop of sodium glycocholate 
solutions at different concentrations. 

at a well defined concentration. This fact was of capital importance 
and the following question immediately arose : what is the significance of 
this minimum? In other words, how is it that in a series of solutions 



Dynes 



76 
75 



70 



65 



60 



55 



















w> 


















































Ini 


,io\i 


v& 


lue 
































































































fi 






































/4 


J 




































/* 


^ 






































^ 








































V 




























































< 


> 












































































































« 





1 

100 



1 

1,000 



1 



10,000 

Concentration 



100,000 ipoo,ooo 



Fig. 29. — Surface tension of serum solutions. Initial values and values after 

2 hours. 



at low concentrations, the static surface tension being materially the 
same for the higher and the lower concentrations a much lower value is 
suddenly observed, and this always at the same concentration for the 
same sample of serum, and in a great number of other cases always in 



DROP OF THE SURFACE TENSION 



69 



TABLE V. 

Surface Tension and Time-Drop of the Surface Tension of Serum 242. 

Temperature 23° C. 



Concentration 





l 


l 


l 


l 


l 


l 


l 


l 


i 


i 




8,000 


8,500 


9,000 


9,500 


10,000 


10,500 


11,000 


11,500 


12,000 


12,500 


n vnp , /Initial value 

Dynes '\ After 2 hrs 

Time-drop 


75.0 

66.0 

9.0 


75.0 

66.5 

8.5 


75.0 

66.0 

9.0 


75.0 
63.5 
11.5 


75.5 
65.5 
10.0 


75.5 
61.0 
14.5 


75.5 
60.0 
15.5 


75.5 
65.0 
10.5 


75.5 
65.5 
10.0 


76.0 
66.0 
100 









n, „ a „ / Initial value 
Dynes ' \ After 2 hrs. 
Time-drop 



1 


l 


l 


i 


l 


9,500 


10,000 


10,500 


11,000 


11.500 


75.0 
58.0 
17.0 


75.0 
58.0 
17.0 


75.0 
57.5 
17.5 


75.0 
56.0 
19.0 


75.0 
57.5 
17.5 



12,000 

75.5 
58.5 
17.0 





l 


l 


l 


l 


i 


i 




9,500 


10,000 


10,500 


11,000 


11.500 


12,000 


n vtlP( , / Initial value 

Dynes. ^ After 2 hrs 


75.5 
58.0 
17.5 


75.5 
59.0 
16.5 


75.5 
58.5 
17.0 


75.5 
56.0 
19.5 


75.5 
58.0 
17.5 


76.0 

60.5 


Time-drop 


15.5 







the immediate vicinity of this concentration? As the quantity of the 
substance acting on the surface tension of water cannot be considered, 
there can only be one cause for the minimum : a critical organisation of 
the molecules. But how is it possible to conceive such an organisation, 
produced always at the same concentration, without admitting that at this 
concentration the molecules are free to organise themselves ? To be free 
they must not be hindered by others, and to reduce the energy of the 
system to a minimum, they must be in contact, without any gaps, like the 
cells in a hive. There must then be just enough molecules to cover the 
surface, but no more. 11 The layer thus formed is then of the thickness 
of one molecule and is obviously only possible at one concentration, 
the other conditions of the experiment being constant. This is produced 
in the above mentioned case at 1/11,000. At 1/10,000, the number of 
molecules being too large, there is some crowding in places. At 1/12,000, 
on the contrary, the number of molecules is too small to cover the 
whole surface and yet keep the same orientation. Channels are formed 

"It is well understood that, as mentioned above, a state of equilibrium must 
exist between the bulk of the solution and the surface but the number of free 
molecules in the solution is negligible in comparison with the number of those 
that are absorbed. 



70 SURFACE EQUILIBRIA 

between large molecular aggregates, floating like ice on the lakes during 
a thaw. An absolute minimum of surface tension can only exist when 
all the molecules are in contact with one another and identically oriented. 
The surface of the liquid is then covered by a solid and homogeneous 
protein film. 



Chapter 3. 
Monomolecular Layer of Serum Constituents. 

Before attempting to measure the thickness of the monolayer (for 
the sake of brevity this expression will be employed in future instead 
of monomolecular layer), it may be of interest to inquire whether it 
cannot be put in evidence by some other method and thus lose something 
of its hypothetical character. 

Such a monolayer should oppose a greater resistance to the escape 
by evaporation of the molecules of the solvent than any other agglom- 
eration of nonorganised molecules. Gaps do not exist in an oriented 



1 

1 

.9 

1 



1 



30 
25 
20 

15 

10 

5 







/ 


\ 






) c 


[y 


V 


N 




226 




i 




M 


1229 


J 


/ 


A 


L 






A 


y 


\f 


\ 






(A 


> — < 


V 


^ 


227- 


-229 

> 



-6 



Concentration 10" 1 to* 2 10' 3 10' 4 10" 5 io" 

Fig. 30. — Diameter of serum solutions in watch glasses after a few hours evapo- 
ration, showing that the solutions to 1 : 10,000 evaporated more slowly than 
the others (cf. Tables I to IV). 



monolayer. Unless, therefore, the surface is agitated or otherwise 
destroyed, it must act to a certain extent as an impermeable membrane. 
On the other hand, at the higher concentrations crannies may exist, due 
to the disorderly piling up of the molecules, and at the weaker con- 
centrations the surface of the liquid will not be entirely covered. With 
the object 'of verifying this fact experimentally, solutions of serum 
in watch glasses were prepared at the following concentrations : 10 -1 , 

7i 



SURFACE EQUILIBRIA 



TABLE VI. 

Serum 226. Expt. No. 1. 

Diameter of Serum Solutions (Rabbit) Evaporating in Watch Glasses. 



Dilution 



Diameter in mm. at 5.41 p.m., after 6 hrs. 

evaporation 

After 30 min 

1 hr 



lO" 1 


lO" 2 


io- s 


io- 4 


10" B 


26 


27 


27 


30 


27 


20 


20 


23 


26.5 


23 








6 


14 






Dilution 



Diameter in mm. at 5.50 p.m. 

After 30 min 

" 40 " 



10" a 



26 

22 





Serum 227. 


Expt. 


No. 2. 










Dilution 


lO" 1 


IO" 2 


io- 3 


10" 4 


io- 5 


10" 6 






Diameter in mm. at 5.42 p.m 


18 



23 

5 


21 
8 


21 
12 


20 



20 


After 50 min 









Serum 228. 


Expt. 


No. 3. 










Dilution 


lO" 1 


lO" 2 


IO" 3 


io- 4 


IO" 5 


IO"' 






Diameter in mm. at 5.45 p.m 


18 



18 



12 



22 
15 


13 



18 


After 30 min 









Serum 229. 


Expt. 


No. 4. 











IO" 1 


IO" 2 


IO" 3 


IO" 4 


IO" 8 





20 


23 


26 


25 





12 


19 


23 


22 








6 


18 


6 



io- 



23 

18 





10~ 2 , IO -3 , 10~ 4 , 10~ 5 , IO -6 . Sometimes the evaporation was allowed to 

take place normally at the temperature of the room and in still air ; at 

other times it was accelerated by means of a weak current of air. Some 

of the results obtained can be found in Tables VI and VII and in Figure 

30. It may be seen that in all cases there is a material difference in 

the rate of evaporation and that the solution 10~ 4 is the slowest to 

evaporate. The experiment was repeated on plate-glass so as to increase 

the surface of evaporation. The results were analogous. (Table VIII 

and Plate VIII.) In working with plate-glass, care should be taken 

to place it in an absolutely horizontal position, otherwise the liquid will 

gather more quickly in one part of the circle with the result that the 

sur trice 

ratio — : will be changed to a large extent and the results vitiated. 1 

volume & * 



1 Lecomte du Noiiy, J. Exp. Med., 1924, XXXIX, p. 717. 



MONOMOLECULAR LAYER OF SERUM CONSTITUENTS 73 



TABLE VII. 

Serum 237. Expt. No. 5. 

Diameter of Serum Solutions (Rabbit) Evaporating in Watch Glasses. 



Dilution 



Diameter in mm. at 2.20 p.m. 

After 5 min 

" 10 " 

" 15 " 

" 20 "... . 

" 25 " ;.*;.'.■." 

" 30 " .... 



io- x 


10" a 


io- 3 


io- 4 


10" 5 


8 


11 


4 


20 


20 





3 





16 


14 











13 


8 











11 














10 














6 





















10"* 

~19~ 
10 








Serum 236. 


(Fan Blowing.) 


Expt 


. No. 


5. 






Dilution 


IO" 1 


10" a 


IO" 3 


IO' 4 


IO" 8 


10"° 






Diameter in mm. at 3.00 p.m 


7 
4 




4 











8 

5 
4 



7 








After 5 min 


o 


7 " 


o 


" 12 " 


o 







Serum 235. (Fan Blowing.) Expt. No. 7. 



Dilution 



Diameter in mm. at 4.39 

p.m 

A.fter 6 min 

" 11 " 

" 21 " 

" 24 " 

" 31 " 

" 45 " 

" 51 " 



io- 1 


10" a 


IO" 3 


10* 


14 


10 


14 


20 


11 





8 


19 


10 








19 


6 








18 











18 











12 











8 















10 



20 
19 
19 
18 

{Became very irregular 
in shape; did not 
wet glass. 



IO"' 



19 

18 

18 

10 











It is easy to understand why the estimation of the rate of evaporation 
had to be made differently in the two cases. For the solutions con- 
tained in the watch glasses, the diameter of the liquid surface was 
measured after a certain lapse of time (several hours) ; for those on a 
plate-glass (mirror glass on which a very thin circumference of a 
diameter of 5 cm. had been traced with a wax pencil so as to keep the 
liquid from spreading) the time which elapsed from the moment one 
of the solutions, no matter which, had evaporated, was counted. A 
study of the tables shows that the solution at 1/10,000 is always the 
slowest to evaporate. In the majority of cases the highest dilutions at 
10" 6 and IO" 5 evaporated first, followed by the concentrations at 10" 1 , 
IO" 2 , 10~ 3 , 10" 4 , in the order named; which proves that in this case 



IWiM^'^i 



o 




-i-j 




J5 


u 


a 


cd 


u 




c 


U 


vi 




o 


u 






g 


s 


o\ 


SO 


u 


u 




c 
c 


Qj 




CO 


rt 


U 








EXPLANATION OF PLATE VIII. 

Fig. 1.— The leveling of the plate was good, and the solutions evaporated evenly, 
drying everywhere at about the same moment save at a small spot near the 
center of the disk, where there was some delay. 

Fig. 2. — The leveling was bad and the solutions started drying on one part of the 
circumference, while the liquid accumulated on the opposite side. 

74 



MONOMOLECULAR LAYER OF SERUM CONSTITUENTS 75 

TABLE VIII. 

Serum 230. Expt. No. 1. 
Evaporation of Serum Solutions (Rabbit). 



Dilution 


io- 8 


10" e 


IO" 1 


10" a 


io- 8 


IO" 4 






Time in min • 





1 


2 


12 


14 


16 











Serum 231. 


Expt 


. No. 2. 




Dilution 


io- 6 


10" s 


io- 1 


IO" 3 


io- 9 


IO" 4 






Time in min 





2 


5 


12 


12 min., 30 sec. 


18 min., 15 sec. 



Serum 237. Expt. No. 3. 



Dilution 


IO" 1 


IO" 3 


IO" 3 


IO" 4 


io- 8 


10"' 






Time in min 





1 


2 


9 


Solutions did not wet the 




glass evenly. 



Serum 236. Expt. No. 4. 



Dilution 


IO" 1 


io- a 


IO" 3 


io- 4 


IO" 8 


10"* 






Time in min 





26 


31 


so 


Solutions did not wet the 




glass evenly. 



Serum 236. Expt. No. 5. 



Dilution 


1/1,000 


1/20,000 


(10- 4 ) 
1/10,000 


1/1,650 




Time in min 





12 


15 


16 







The figures indicate the number of minutes which were required by each solu- 
tion to dry, the zero time being taken when one of them, no matter which, dried 
first. 



the decrease in the vapour pressure of the solution does not play a 
primary part in the phenomenon. According to Raoult's law, solutions 
at very low concentrations IO -6 and IO" 5 should indeed evaporate more 
rapidly, but the solutions at 10 -4 and IO" 3 , etc., should follow in succes- 
sion, whereas it is the opposite which actually occurs. 

There are other facts in favour of the existence of a protein mono- 
layer; in particular certain phenomena of crystallisation. These will 
be dealt with later (Chapter 6, Crystallisation). The writer, of course, 
does not intend to infer that this layer is composed of pure proteins; 
the lipoids and other constituents of the serum are also present, but 
they are probably linked in some unknown way to the proteins. 



76 SURFACE EQUILIBRIA 

The objection might be made that together with the fatty acids, the 
lipoids are the principal factors in the drop of the surface tension of 
serum. A little further on, however, it will be shown that at similar 
concentrations crystalline egg albumin and the isolated proteins of serum 
show a drop in surface tension of the same order of magnitude. There 
can therefore be no question that the drop in surface tension is mainly 
due to the proteins. As mentioned above, the lipoids and fats are prob- 
ably an integral part of the serum "molecule" in solution, but at the 
present time it is impossible to define the nature of the force which 
binds them together. 

Thickness of the Monolayer of Serum. 1 

With the information now available it is possible to attempt to cal- 
culate the thickness of the monolayer of serum and consequently the 
mean length of the molecules which compose it. Besides the exact 
concentration at which the minimum is produced, it is necessary to 
know the actual concentration of the serum and the density of the 
anhydrous proteins. (The term "protein" is employed but all the con- 
stituents of the serum are considered, including the free amino-acids 
which are to be found in very small proportion, and the lipoids which, 
a^ was stated above, cannot be considered as normally existing in a 
free state in the serum or the plasma. It would be more exact to speak 
of "molecules of serum" if this term did not appear too vague by reason 
of its complexity.) Furthermore it is necessary to know if the mole- 
cules are adsorbed on the glass as well as in the free surface of the 
liquid. This last point will be elucidated first. 

As has already been pointed out, the position of the minimum evi- 
dently depends on the ratio — : of the liquid in the watch glasses. 

Indeed each concentration corresponds to the presence of a certain 
number of molecules per cc. of liquid. If we assume that all the 
molecules are adsorbed, that is displaced from the bulk of the liquid 
towards the periphery, 2 and if we consider 1 cc. of liquid, we may say 

^ecomte du Noiiy, J. Exp. Med., 1924, XL, p. 133-149. 

3 This hypothesis is in conformity with the opinion of the best authorities 
whenever very high dilutions are considered. It is certain that all the molecules, 
in the strict sense of the word, are not adsorbed, but it is extremely probable 
that there remain less than 1 per thousand in the liquid when equilibrium is 
established. Now we shall see later that the admitted sum of experimental 
errors is of an order of magnitude such that even should there remain in the 
liquid a number ten times higher, that is 1%, there would result a negligible 
error in the value of the thickness which is to be calculated. Unfortunately the 
Gibbs-Thomson law has not been verified quantitatively in the case of proteins; 



MONOMOLECULAR LAYER OF SERUM CONSTITUENTS 77 

that if all the molecules which it contains are geometrically disposed side 
by side in a single layer, they will occupy a surface S, and cannot in any 
case occupy a larger or a smaller surface, otherwise there would be gaps, 
piling up, or a change of orientation. So that if the molecules contained 
in 1 cc. of liquid are to cover a double surface, or 2S, it will be neces- 
sary to double the number of molecules ; which amounts to saying that 
the concentration is doubled. The same reasoning indicates that it 
would be necessary to triple and quadruple the concentration so as to 
cover with a monolayer a surface three and four times larger. If, on 
the contrary, it is the volume which increases and not the surface, 
if we use 2 cc. of solution in a vessel with a surface ^ (the concentration 
being the same as that of the sample cited above), we shall have double 
the number of molecules and in order to obtain a monolayer it will be 
necessary to divide the concentration by 2. This means, in short, that 
the position of the minimum, or the existence of the monolayer, depends 

on the ratio — : == j/- ^ n changing this ratio it should be possible 

to change the position of the minimum, that is to say the concentration at 
which the minimum should occur. Consequently by maintaining the 
free surface of the liquid constant, or about equal to 13.10 cm. 2 , and 
by varying the surface of the glass (the volume being constant), a dis- 
placement of the minimum should be observed if there is adsorption on 
the glass and, on the contrary, no displacement if there is no adsorption, 
for in that case the adsorbing surface will not have changed. When 
increasing the surface of the glass, the displacement of the minimum 
(if produced) should occur toward a higher concentration and the ratio 
between the two surfaces of adsorption should be the same as the ratio 
between the concentrations. 

Adsorption on the Glass. 

To realise these conditions experimentally we used the same watch 
glasses. A solution of serum diluted at 1/11,000 (concentration at 
which the minimum occurred with this particular rabbit serum) was 
poured in a first series of glasses ; in a second series 500 small glass 
beads were placed side by side. These beads were carefully chosen so 
that their total surface should be known as exactly as possible. Fifty of 
them were measured with micrometer calipers to 0.01 mm. Their 

but it is beyond doubt that the state of equilibrium of colloidal solutions corre- 
sponds to an almost complete displacement of the molecules and that less than 
1% remain in the solution. 



78 



SURFACE EQUILIBRIA 



diameter varied from 0.90 to 1.00 mm. The mean value of the diameter 
of the fifty beads was 0.95 mm. Two series of fifty gave the same 
mean value. The mean surface of one of these beads was therefore 
0.02847 cm. 2 The total surface of glass was thus 13.33 (surface of 
the watch glass) + 14.235 = 27.56 cm. 2 in round figures. The total 




Dynes 

75 
73 
71 
69 
67 
65 
63 
61 
59 
57 



6,000 7,000 6,000 9,000 10,000 11,000 12,000 

Concentration 

Fig. 31. — Shift of the place of the minimum value of static surface tension, 
as a consequence of the increase of the surface of adsorption; i.e., the ratio 
S 




is increased. (Serum) 



surface of adsorption was 27.56 + 13.08 (surface of the liquid) = 
S' = 40.64 cm. 2 The ratio -r? = 20.30 instead of 13.2. According to 

the above statement, the concentration at which the minimum should 

S' C 

be produced if there is adsorption is given by the formula -=- = -pr 

(C being the unknown concentration). Under these conditions C is 
calculated to be approximately equal to 1/7,000. The minimum must 
therefore be looked for around 1/7,000 if there is adsorption on the 
glass and around 1/11,000 if there is no adsorption. Figure 31 and 
Table IX give the results of a series of experiments and show clearly 



MONOMOLECULAR LAYER OF SERUM CONSTITUENTS 79 



TABLE IX. 

Surface Tension and Time-Drop of Serum Solutions in Saline in Standard 

Watch Glasses. 





Serum 232. 














Concentration 


l 

6,000 


1 


1 


1 


1 


1 


1 


1 


1 


7,000 


8,000 


9,000 


10,000 


10,500 


11,000 


11,500 


12,000 


With 500 glass beads in watch-glasses. 



Initial value 

Value after 1 hr. 
Time-drop (1 " ) 
Value after 2 hrs. 
Time-drop (2 " ) 



73.5 


75.0 


75.5 


75.5 


76.0 


76.0 


76.0 


76.0 


61.8 


60.0 


61.0 


61.0 


62.0 


62.2 


62.2 


63.0 


11.7 


15.0 


14.5 


14.5 


14.0 


13.8 


13.8 


13.0 


60.5 


59.0 


60.0 


60.5 


60.5 


61.8 


61.8 


61.8 


13.0 


16.0 


15.5 


15.0 


15.5 


14.2 


14.2 


14.2 



76.0 
62.2 
13.8 
61.0 
15.0 



Control 1, without beads. 



Initial value 

Value after 1 hr. 
Time-drop (1 " ) 
Value after 3 hrs. . 
Time-drop (3 " ) 



74.0 
62.0 
12.0 


73.0 
60.5 
12.5 


73.5 
59.0 
14.5 


7X5 
59.0 
14.5 


75.5 
60.5 
15.0 


73.0 

59.0 
14.0 


76.0 

58.0 
18.0 


73.5 
58.0 
15.5 


60.0 
14.0 


58.0 
15.0 


58.0 
15.5 


58.0 
15.5 


58.5 
17.5 


58.5 
15.0 


S7.5 
18.5 


57.5 
17.0 



73.5 
59.0 
14.5 
58.0 
15.5 



Control 2, without beads. 



Initial value 

Value after 1 hr. 
Time-drop (1 " ) 
Value after 3 hrs. . 
Time-drop (3 " ) 





75.0 


74.5 


75.0 


75.5 




76.0 






59.0 


59.0 


59.0 


60.0 




58.0 






16.0 


14.5 


16.0 


15.5 




18.0 






58.5 


58.5 


58.5 


58.5 




57.5 






16.5 


15.0 


16.5 


17.0 




18.5 





75.5 
60.5 
15.0 
59.0 
14.5 



that the minimum has been shifted towards 1/7,000. Therefore it may 
be admitted that there is adsorption on the glass. 

In order to confirm the preceding results a control experiment was 
made in which instead of the surface of the glass being greatly increased 
and the volume of the liquid remaining constant, the volume of the 
liquid was increased proportionately much more than the surface of 
the glass. For this purpose it was necessary to use cylindrical glasses 
(Petri dishes) the diameter of which was about equal to that of the 
liquid in the watch glasses but which held a larger quantity of liquid. 
The diameter of the Petri dishes used was 4 cm. ± 0.05. The depth 
of 8 cc. of solution was about 0.63 cm. The total surface of adsorption, 
including that of the glass, had a mean value of 33.1 cm. 2 , and the 
surface of the liquid alone very nearly 13.0 cm. 2 If it be assumed 
that adsorption only takes place in the free surface of the liquid, its 
surface being the same as in the watch glasses and the volume V being 



80 



SURFACE EQUILIBRIA 



increased fourfold, the concentration should be four times less, i.e. 

1/44,000. On the other hand, if adsorption also takes place on the 

9 33.1 

glass, the ratio jz = R' = —- = 4.15 ; hence the maximum should 

occur at 1/35,000. As the thickness of the liquid was much greater 
than in the watch glasses, more time was allowed to elapse between the 
two measurements of surface tension (20 to 21 hours). Figure 32 



Dynes 
58 

56 
54 





















•— ■ 


►— 


v emits a| ,er c 
\ k—k k — i 


,1 tlOUPS 


1A 




\ 


y 


K-— ' 


»-~ - 


c 


< 


1 


B 




\ 


-^~ 















1 



1 



3QJ300 



34P00 36JD00 AZPOO 
Concentration 



4^000 



Fig. 32. — Shift of the minimum due to a decrease in the ratio 



V 



(Serum) 



shows that the experiments again indicated that adsorption took place 
on the glass, as a sharp minimum was observed at 1/35,000, or very 
near that point. The differences were of the order of magnitude of 
experimental errors. These latter experiments are more delicate than 
those with the watch glasses, as it is very difficult to maintain the 
surface of 8 cc. of liquid perfectly stable and free from ripples. It is 
superfluous to add that during the whole experiment the solutions were 
protected against evaporation by a glass cover. 

Percentage of Proteins in Rabbit Serum. 

The percentage of proteins in the serum was determined by the 
Kjeldahl method (nitrogen titration) and found equal to 6.51 per cent. 
This figure agrees well with the data published by Mathews 3 and 
Arthus 4 (total nitrogen 1.080 per cent; non-protein nitrogen 0.038 
per cent). 



Specific Gravity of Anhydrous Proteins. 

A sample of the serum used was dialyzed during four days to de- 
prive it of its salts. It was then dried in a desiccator in vacuo and the 



263. 



8 A. P. Mathews, Physiological Chemistry, N. Y. 2nd Ed. 1916, pp. 261 

5. 

* M. Arthus, Precis de Chimie Physiologique, Paris, 5th Ed. 1908, p. 147. 

a' 

y 



MONOMOLECULAR LAYER OF SERUM CONSTITUENTS 81 

resulting shellac-like flakes were placed in different mixtures of benzene 
and chloroform. The specific gravity of the mixture, in which the flakes 
floated without moving up or down, was found to be 1.275, which was, 
therefore, the specific gravity of the proteins. Three different sera gave 
the same value. Under identical conditions, other measurements made 
at different intervals always gave similar figures. 

Calculation of the Thickness. 

The serum containing 6.51 per cent of proteins is diluted to 1/11,000 

(concentration at which the minimum corresponding to the assumed 

monolayer is produced, as indicated by the minimum of surface tension). 

The final dilution of the dry substance is 1/169,000. 2 cc. of the solu- 

2 
tion are used in every watch glass, that is -. ^ Q nm = 0.00001184 gm. of 

proteins per watch glass. This weight of proteins (11.84 X lCh 6 gm.) 
is spread evenly, according to the hypothesis, on an area of 26.4 cm. 2 
(monolayer). Thus the weight of proteins per cm. 2 will be 11.9 X 
10~ 6 -^26.4 = 4.48 X 10~ 7 cm. If the specific gravity of these substances 
were equal to 1, the thickness of the monolayer would be 4.48 X 10~ 7 cm. 
But it is equal to 1.275: consequently 4.48 X 10~ 7 must be divided by 
1.275, and we obtain 3.514 X 10~ 7 , or 3.514 uu. for the thickness of the 
monolayer of total proteins in this serum. This figure represents the 
mean value of the length of albumin and globulin molecules. The 
thickness of the monolayer of a total serum (including amino acids, 
etc.) was found to be 4.05 X 10~ 7 cm., or 4.05 u|i, approximately.* 

The position of the minimum changes only slightly in different experi- 
ments. This is a consequence of the relative constancy in the concen- 
tration of proteins. But the absolute value of this minimum varies 
to a fairly large extent (between 52 and 60 dynes generally for rabbit 
serum). We shall see later on (Chapter 6) that one of the most impor- 
tant factors of these differences is a physico-chemical modification of 
certain proteins of the serum as a consequence of immunisation. The 
highly complicated serum molecules may not all be able to orient them- 
selves identically, which would be another factor for these differences. 
Indeed, a certain proportion of molecules may be associated or disposed 
horizontally and this would tend to shift the minimum. As, however, 
most of the experiments were made with only eleven different dilutions 

* Note. The value of the specific gravity obtained for serum flakes does not 
correspond exactly to that of the whole serum on account of the solubility of 
fats and lipoids in chloroform and benzene. However the error does not amount 
to 1 per cent. 

Id 



$2 SURFACE EQUILIBRIA 

ranging between 1/7,000 and 1/12,000, the shift was too small to be 
observed. When the number of dilutions was increased to 30 between 
1/9,000 and 1/12,000 (the steps being 1/9,000, 1/9,100, 1/9,200, 
etc.), it was found that in a few cases the minimum had indeed been 
shifted by an amount which could not be calculated exactly on the 
basis of the percentage of proteins. The resulting error in the 
estimation of the thickness of the monolayer was 0.03 X 10~ 7 , or a 
little less than 1 per cent. As this error is smaller than the order of 
magnitude of the errors involved in the experimental procedures, it 
may well be neglected and only the first decimal point need be considered. 

Significance of the Critical Concentration at Which the Minimum 
Is Observed. 5 

The problem now arises as to whether this critical concentration 
near 1/11,000, corresponding to a maximum action of the serum pro- 
teins on the surface tension of the water in our vessels, is the conse- 
quence of an arbitrary conjunction of several factors, or whether it has 
some deeper significance. 

The proposed hypothesis of an oriented monolayer makes it possible 
to approach the problem in a simple way. We have seen that this 

critical concentration depends among other factors on the ratio -77 of the 

solution. In order to maintain the integrity of a monolayer the con- 
centration must increase, all other conditions being equal, when this 

S . 

ratio -JZ increases. This ratio increases when the volume decreases. 

In a sphere 1 mm. in diameter it is equal to 25. Should the diameter 
be 0.1 mm. it becomes 250, and 2.500 if the diameter is again decreased 
to 0.01 mm. It is minimum for a sphere and therefore becomes larger 
still if the shape of the vessel is different ; if, for instance, the sphere 
is flattened. From the last preceding figure it follows that the concen- 
tration of serum should be 190 times greater than in the watch glass 
in order to build up a monolayer in a sphere the diameter of which is 
0.01 mm. In other words it should be 1/58 instead of 1/11,000. 

The question can now be put in the following manner : what should 

S 
be the dimensions of a container in which the ratio 77 would be such 

that the surface active molecules of undiluted serum could be adsorbed in 
an oriented monolayer? In other words, a vessel in which this ratio 

8 Lecomte du Noiiy, C. R. Ac. 1923, 177, p. 1140. J. Exp. Med. 1924, 
XXXIX, p. 37; and C. R. Soc. Biol. 1924, XC, p. 1450. 



MONOMOLECULAR LAYER OF SERUM CONSTITUENTS 83 

would be 11,000 times larger than in a watch glass, i.e. 145,000. It was 
found that provided the shape (flat disc) remains unchanged, it would 
require a diameter of 5 |x (0.0005 cm.) and a maximum thickness of 
0.2 fx. The diameter happens to be of the order of magnitude of small 
living cells, though the thickness is about ten times less ; but our calcu- 
lation does not take into account the existence of other adsorbing sur- 
faces inside the cell (nucleus, mitochondria, etc.) which would increase 
the ratio considerably and might easily account for the discrepancy. 

We might look at the problem from a different angle and no longer 
consider the liquid contained in the cells, but the surrounding liquid; 
i.e. the plasma in the arteries and especially in the capillaries. Assum- 
ing that in small capillaries the cells almost obstruct the vessels, which 
is the case as shown by microscopic examination of transparent flaps 

S . . 

in live frogs, the calculation gives a ratio of -= which varies according to 

the diameter, the flattening of the capillaries and the number of red 
corpuscles, between 50,000 and 200,000. 6 These figures seem to indi- 

8 Of course, these conditions may be considered as somewhat arbitrary, and 
it is not our aim to lay emphasis on the quantitative agreement of these figures. 
However, very little is known concerning the concentration of red and white 
cells in the capillaries. It varies according to circumstances, probably within 
great limits. C. S. Danzer and D. R. Hooker (Am. Jnl. Physiol, 1920, LII, p. 136) 
found that one of the annoyances in determinations of the capillary blood pressure 
in man, when the criterion employed was the cessation of corpuscular flow, lay 
in the fact that often the large and conspicuous capillaries were filled with stag- 
nated corpuscles, and they noted that in the course of the observations it was not 
uncommon to find that a previously stagnated vessel had become patent and 
that, on the other hand, patent vessels became stagnated. In a recent contribu- 
tion, A. Krogh (Jnl. Physiol. 1918-19, LII, p. 457) reached the conclusion 
that in muscle at rest many capillary channels are occluded. Moreover, it must 
be borne in mind that the calibre of capillaries is constantly changing and that 
the changes are independent of the pressure of the blood supplied to them, as was 
observed as early as 1879 by C. S. Roy and J. G. Brown (Jnl. Physiol. 1879-80), 
II, p. 323). The variations in the diameter of capillaries at rest and during stimu- 
lation have been reported by E. Steinach and R. H. Kahn (Arch. Ges. Physiol. 
1903, XVII, p. 105). They observed, as did D. R. Hooker, an average decrease 
in diameter of from 18.5 to 7.8u. (Physiol. Rev. 1921, I, p. 112). Interpreting 
these values in terms of sectional area, the cross section of the relaxed capillary 
is found to be 0.0002 sq. mm. for the contracted capillary, a five-fold difference. 
Capillaries under 10u. are not so frequently observed to contract; nevertheless, 
Steinach and Kahn noticed vessels of 10u. reduced to 3 to 4u. in diameter under 
stimulation. However, conditions are quite different when serum circulates in 
capillaries and when it stands diluted in a watch glass. The orientation and 
consequently the space occupied by the adsorbed molecules are possibly a function 
of the nature of the boundary, and may be different in the case of air, glass and 
endothelial cells. 

For these reasons, no accurate coincidence of figures can be expected and if a 
satisfactory accord is found, it must not be looked upon as a reliable expression 
of the facts, but simply as an indication concerning the order of magnitude. 
Therefore, it may be stated that if it be assumed that the maximum time drop 



84 SURFACE EQUILIBRIA 

cate something more than a simple coincidence. We are led to admit 
the possibility of the existence of a polarised layer of active molecules 
on the walls of the cells in general. Conceivably the wall of the cell 
itself is not the only membrane which separates the inside from 
the surrounding fluid ; a protective, chemically active film envelops 
it. Hence it can be easily understood that this kind of thin (3.5 to 
4 u|i), unstable and reacting filter, which is formed of fragile elements, 
real intermediaries between the products carried by the circulation 
and the endothelial cells, would enable extremely small quantities of 
substances to act on the entire system. For the identical orientation 
of the molecules would allow the local disturbances to be summed up 
and propagated. The slightest local reaction affecting the equilibrium of 
the atomic structure of the molecule, or of a series of oriented mole- 
cules, would be perceived far beyond the seat of the reaction because the 
change brought about in the field of forces of a single or a series of 
molecules will affect a large surface of the monolayer. 

If the plasma were flowing into a capillary vessel the walls of which 
had not yet adsorbed their monolayer, it would be almost completely 
deprived of its proteins and comparable to water. But as soon as this 
layer is formed, the withdrawal of the proteins ceases and the concen- 
tration becomes normal. It is possible that under certain conditions 
other layers can be formed on top of the monolayer, which, however, 
is the only one to be polarised, whilst the non-organised layers are easily 
removed. For instance, erythrocytes placed in Ringer solution will 
lose their supplementary layers, if there are any, but retain their 
monolayer. 

Such an oriented monolayer will act as an electric condenser and it 
is easy to understand that any reaction affecting the fragile atomic 
structure of the adsorbed proteins will produce a variation in its electric 
charge. As a result, one of the phenomena known as agglutination, 
precipitation or hemolysis could follow. For instance, hemolysis will 
take place when the integrity of the condenser is destroyed. This may 
be brought about by a number of different causes ; mechanical rupture 
of the monolayer, change in the dielectric constant of the protein, im- 
portant changes in one of the charges as a result of chemical reaction, 

in the surface tension of a serum solution is due to the organisation in an 
oriented monomolecular layer of certain active constituents of the serum, it is 
probable that such a layer corresponds to the optimum activity of these molecules, 
as there is no piling up or overlapping. Consequently it is logical to think that 
in an animal the concentration of the body fluids will be such as to permit their 
optimum activity. 



MONOMOLECULAR LAYER OF SERUM CONSTITUENTS 85 

etc. Agglutination may happen when only a slight change in the super- 
ficial charge occurs as a consequence, for instance, of the adsorption 
of substances carrying a charge of different sign. 

It has been stated above that, according to our hypothesis, the thick- 
ness of the adsorbed layer was of the order of 35 angstroms or 3.5 \i\i. 
If all the amino-acids, lipoids, fats, etc., are included, it would be equal 
to about 40 angstroms. It is not without interest to mention the re- 
sults obtained by Fricke. 7 By using an entirely different method, based 
on the measurement of the electric resistance of a suspension of red 
cells in Ringer solution, he arrived at the conclusion that the thickness 
of the membrane of the red cells was 33 angstroms. This order of 
magnitude (3 ten millionths of a millimeter) cannot possibly be con- 
sidered as applying to a real membrane. The similarity of the figures 
would therefore indicate that what Fricke measured was really the 
thickness of the monolayer, which view he has recently adopted. 8 Dr. 
Fricke assumed, and his measurements have proved the existence on 
both sides of the "membrane" of two electric charges, equal in value and 
opposite in sign. It is impossible to explain otherwise the values ob- 
tained. The identical orientation of the molecules, forecast by the 
writer in 1922, 9 is a necessary consequence of Fricke's experiments. 
However, these figures must not be considered as rigorously accurate. 
They merely indicate an order of magnitude. But we may safely say 
that, considering the precision of the experiments, 4.1 \i\i may be taken 
as an upper limit, and 3.3 [i\x as a lower limit of the thickness of the 
adsorbed monolayer. It will be shown later (Chapter 7) that when 
serum is diluted in physiological salt solution, the proteins adsorb part 
of the salt and carry it to the adsorbing surfaces. 10 There is therefore 
reason to think that the oriented monolayer also contains a certain pro- 
portion of salts. 

7 Hugo Fricke, Jnl. of Gen. Physiol. 1924, VI, p. 375. 

8 Hugo Fricke, Phys. Rev. 1925, XXVI, p. 682. 

9 Lecomte du Noiiy, J. Exp. Med. 1922, XXXV, p. 707. It seems that 
the idea of the orientation of molecules at the surface of pure liquids and 
solids was proposed for the first time by Hardy in 1912. In the following para- 
graph he alludes to it in a general way. (Proc. Roy. Soc. 86 A. p. 634). "If 
the stray field of a molecule, that is, of a complex of these atomic systems, be 
unsymmetrical, the surface layer of fluids and solids, which are close packed 
states of matter, must differ from the interior mass in the orientation of the axes 
of the fields with respect to the normal to the surface, and so form a skin on the 
surface of a pure substance having all the molecules oriented in the same way, 
instead of in purely random ways." 

10 Lecomte du Noiiy, J. Exp. Med. 1922, XXXV, p. 707; and C. R. Ac. 
1922, CLXXIV, p. 962. 



Chapter 4. , 

Sodium Oleate — Dimensions of the Molecule — 
Calculation of the Constant TV of Avogadro. 

Although we were able to demonstrate experimentally that the mole- 
cules of the substances contained in blood serum and those of egg 
albumin were adsorbed on the glass in the free surface of the liquid, it 
did not follow, a priori, that such would be the case with sodium oleate. 
It was necessary, therefore, to experiment along the same lines with 
the latter substance, in order to find out whether the surface of the 
glass would have to be taken into account in the calculations or whether 
only the free surface of the liquid was involved. Consequently the 
same procedure was followed as in the case of serum. However, beads 




Vefo.ooo 

Mean value of jromiroa,- 7(306,000 



t^ | nean yaaue o] jraiTiima,' /wv,vvv | 

550,000 5T5p<50 600,000 6257550 600,000 6?550T) TOWO 7?JpO 750,000 775^00 55(p0 

Dilution 

S 
Fig. 33. — Shift of the minimum due to an increase of the ratio vy- (Sodium 

Oleate) v 

of a larger diameter but in smaller numbers were used. Fifty beads, 
the mean area of which was 0.158 cm. 2 were placed in a watch glass. 
The total surface of adsorption became 32.7 cm. 2 instead of 26.4 cm. 2 
which, in the case of adsorption on the glass, ought to have shifted the 
first minimum from 1/750,000 to 1/605,000 approximately. Figure 33 
gives the result of five consecutive experiments. A parallel experiment 
was made with Petri dishes the diameter of which was very nearly equal 

86 



SODIUM OLEATE— DIMENSIONS OF THE MOLECULE 87 



6 80 

| 75 

J, 70 

66 

60 



1,000,000 





















































Qoaium oieate 














01>s. tni-n. 
Calcui. • 




,' 












t 


t 




,' 










Diff. per> cent 




-2 












-2.7 




+1.2 
















-:> 


\ 




if 


"Sr^*-^ 


\ 


/\/ 


!=^r< 












' 




s 




'1 










V 


y 


















o 




















tf 

































































































2,000,000 



3,000,000 
Dilution 



4000,000 



Fig. 34. — Shift of the three minima of sodium oleate, due to a decrease in the 

S 
ratio ^j. See also Figs. 35, 36 and 37. 





Sodium oleate 
























"Mean 












> 

?T 8 




Otos. min. 
Calcui. ■ 
Diff. per cent 




t' 


















f 










-2 








+0.1 
Observed min 


ima 


-1.2 












gs 






















— g— 


--9-= 


70 
65 
60 






\07 


><_- 






































\ 
















































I 




1 




> 


1 




1 




1,00( 


VJ00 


2,00( 


}ooc 


^ooc 


;ooc 


4,O0C 


,000 



Dilution 

Fig. 35. 




1,000,000 



2,000,000 



3,000,000 

Dilution 

Fig. 36. 



4,000,000 



88 



SURFACIi EQUILIBRIA 



to that of the free surface of the liquid in the watch glasses, that is, 
42 mm. As in the case of serum, 8 cc. of solution were used instead 

of two and in each glass the ratio -=z was equal to 4.48. The same cal- 
culation as that made previously (page 78), showed that the minimum 
should be shifted to 1/2,225,000, if adsorption took place on the glass, 
and to 1/3,000,000 if there were no adsorption on the glass. Figures 
34 to 37 show that adsorption must take place on the glass since the 









































































Obs. min. 
C alcut • 


T 


t 














i_ 














75 


















































^J 




fc=j 


p*^ 


=«^ 


-^ 


>=4 


>-~=4 


\< 
















70 
65 






^^ 








* 



















































































1,000,000 



2,000,000 



3,00 0,000 

Dilution 



4000000 



Fig. 37. 

minimum is indeed observed at about 1/2,225,000. The shift of the 
second and of the third minima which may be interpreted as being due 
to a monolayer of horizontal molecules, is also observed to occur 
at the concentration very near that which was calculated on the basis 
of adsorption on the glass, namely, at 1/3,600,000 instead of 1/4,900,000 
and at 1/4,100,000 instead of 1/5,600,000/ in round figures. 



1 The preceding experiments were repeated a great number of times and are 
subject to the same observations as those that follow on sodium oleate. They 
clearly illustrate the fact that the concentration is not the only factor which 
determines the value of the surface tension of certain colloidal solutions. An 
absolute minimum of the static surface tension of these solutions can always be 
observed at any concentration, provided that it be contained in a vessel the ratio 
c 
— of which is such that the organisation of a monolayer is possible; in other 

words, when the following equation is verified for a given substance: 



Ca 2 = m^ 



where C = concentration, a 
of the molecule 



area of a cross-section of the molecule, tn = mass 

total surface of ad- 



molecular weighty N = ^ x ^ ^ 



sorption. V = volume of the solution. For instance, in the case of sodium 



oleate, C = 1/750,000, for 



V 



13.2 and C 



1/2,225,000, for ^ = 4. 



or C 



SODIUM OLEATE— DIMENSIONS OF THE MOLECULE 89 

These experiments, although rather difficult of realisation, are con- 
vincing. There can be no doubt that in the case of sodium oleate, as 
in that of the proteins studied previously, adsorption takes place on 
the whole surface of the liquid in contact with air or with glass. The 
works of Griffin 2 and of Harkins and Zollman 3 show that adsorption 
takes place at the surfaces of contact of liquids such as kerosene and 
benzene. Consequently, the same calculations which were used in order 
to determine the thickness of the monolayer of serum molecules may be 
applied to calculate the dimension of sodium oleate molecules. 

Study of Sodium Oleate. 4 

The samples of sodium oleate used in the following experiments 
were prepared with the utmost care in our laboratory by Dr. L. E. 
Baker. Nevertheless it is sometimes difficult to reproduce exactly the 
same phenomena. Solutions of sodium oleate have been observed to 
act in a different way so far as the equilibrium of their superficial layer 
was concerned, and the cause of these discrepancies is not always easy 
to elucidate. A fairly large number of experiments showed no minima 
but in all our experience we never made an experiment the results of 
which were contradictory to the positive results in showing minima 
at unexpected concentrations. There are two main possible causes for 
negative results; the spontaneous formation of the insoluble isomer 
(sodium elaidate) and the fixation of C0 2 . Certain samples of sodium 
oleate will dissolve readily and give at a concentration of 1 per 1000, 
a perfectly clear solution with no appearance of colloidality. The 
Tyndall cone obtained with a thin and intense beam of light is very 
weak and hardly visible. Such a solution kept under nitrogen, pre- 

S S 

1/4,450,000 for —=2.24. If =r =1000 the same minimum would occur at 

S 
1/9,900; and in general, for a given orientation, C — = K, (the value of C 

being taken as the denominator of the fraction expressing the concentration). 
K is a constant characteristic of every substance and of each possible orientation. 
For sodium oleate there are consequently three constants : KiK 2 K 3 ; Ki = 99 X 
10 B , K 2 = 161 X 10" 5 , K 3 = 183.5 X 10" 5 , approximately. These three coefficients 
are proportional to the area of the three cross sections of the molecule, a 2 , b 2 , 
and c 2 , so that 

Ki K.2 Ivs 

2 E. L. Griffin, J. Am. Chem. Soc. 1923, XLV, p. 1648. 
8 W. D. Harkins & H. Zollman, J. Am. Chem. Soc. 1926, XLVIII, p 69 
4 Lecomte du Nouy, Phil. Mag, 1924, XLVIII, p. 664-672; and J. de Phys et 
le Radium, 1925, VI, Ser. VI, p. 145-153. 



90 



SURFACE EQUILIBRIA 



ferably in the ice-box. will maintain its limpidity tor many weeks. 5 
The results of a series oi experiments obtained with perfect samples 
will be found in Table X. 

TABLE X. 

Concentrations at Which the Minima Occurred in a Series of Consecutive 
Experiments. The Amplitude of the Drop Is Equal to the Difference 
Between the Values of the Dynamic and the Static Tensions. (Fig. 38.) 



Experiment 



1 

2 

3 

4 
5 

6 
7 
8 
9 

to 



1st Minim 



1 750,000 

i 7^.<y^ 

1 749.000 

i 750,000 

1 749.000 

1 751.000 

1 751.000 

1 750.000 

1 750,000 

1 750.000 



Drop 



12 dynes 

IS ' " 

10 " 

20 " 

12 " 

| 12 « 

15 " 
20 " 

16 " 
7.1 



2nd Minim Amplitude, 3rd Minim ! Drop 



1 1.220.000 

1 1.220.000 

1 1.220.000 

1 1,222,000 

1 1.220,000 

1 1.220.000 

1 1.222.000 

1 T. 220.000 

1 '1.213.000 

1 1.221.000 



10 dv 
15 

16 
g 

23 

10 

S 

12 

8 
10 



nes 1 1 
" 1/1 

" |11 
"111 
- ' 1 1 
1 1 
" 1/1 
" \ 1 1 
" | 1 T 
" 111 



.390.000 
,390.000 

,380,ooo 

,391,000 
,390,000 
,390,000 

,395,000 
.386.000 

.390,000 
,390.000 



4 dvnes 



Figure 38 expresses the result of a typical experiment. It may be 
observed that when, as a result of imperfect wetting of the glass, or 



5 The following technique for preparing sodium oleate was finally found to be 
quite satisfactory : Oleic acid having a theoretical iodine number is prepared 
first from Kahlbaum's oleic acid as follows : 23 gm. are dissolved in 750 cc. of 
50% alcohol in a 2 litre flask. To this is added, gradually and with constant 
stirring, 1 litre of boiling lead acetate solution I 300 cc. 10% acetate diluted to 
1 litre) and the mixture shaken for ten minutes. It is then cooled under running 
water while rotating the flask so that the precipitate adheres to the sides and the 
supernatant liquid can be easily decanted. The precipitate is thoroughly washed 
three times with boiling water (1 litre being used for each washing). The 
precipitated lead salts are then dissolved in 750 cc. of purified ether warming 
under a reflux to aid solution. When cool, the lead salts of the saturated fatty 
acids are filtered off. and the ether solution of lead oleate decomposed by shaking 
in a separatory funnel with 10% hydrochloric acid, repeating this operation until 
no more lead chloride precipitates. The ether layer is washed with distilled 
water until free from acid. The ether is evaporated on a water bath under an 
atmosphere of C0 2 . or nitrogen. The oleic acid is freed from water by cooling 
and its iodine number determined by the Wijs method. If the process has been 
carefully carried out, a theoretical iodine number (e.g., 90) will be obtained. 

Sodium oleate is prepared by adding to a weighed amount of the above oleic 
acid dissolved in alcohol, a quantity of alcoholic sodium hydroxide slightly in 
excess of the equivalent weight, adding it slowly from a burette and boiling 
under a reflux condenser for twenty minutes. It is important that the quantity 
of alcoholic sodium hydroxide be determined by calculation and not by deter- 
mining the end point of the reaction by an indicator. The strength of the sodium 
hydroxide solution must be determined by titration just before use. The sodium 
oleate is precipitated by cooling in the ice-box. recrystallised twice from absolute 
alcohol and dried in vacuo over calcium chloride. The ether solutions must not 
stand at room temperature in the light, but be kept in the dark in the ice-box 
under C0 2 or nitrogen. 



SODIUM OLEATE— DIMENSIONS OF THE MOLECULE 91 

of a slight error in the estimation of the concentration due to imperfect 
stirring, or of particles of dust on the liquid, etc., the minimum does 
not occur exactly at one of the three critical concentrations ( 1/750,000, 
1/1,220,000, 1/1,390,000), it is merely slightly shifted, i.e. the magni- 
tude of the drop is smaller. 



Dynes 


























































































pep cm. 
















































































































































































































































































































































































































s 


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1 11 11 1 
5.000 iO^OS 50,000 ioo^ooo 500,000 1,000,000 
" 3 10" d 10" 5 10" 5 


i 


l l 

£,000,000 2,500,000 


l 


3 
10 


10 


1,5 


:■■: 


j: 


:,::■:.:•: 



ConcentPation 



Fig. 38.— Dynamic and static values of the surface tension of sodium oleate 
solutions, at concentrations ranging from 1/1,000 to 1/3,000,000. Temp. 22°. 



A complete protocol of a consecutive series of measurements will be 
found in Tables XI, XII, and XIII. These experiments, made with less 
perfect samples of sodium oleate, are far from yielding such con- 
sistent results. They are published, however, so that the reader may 
see for himself that if the mean values of a sufficiently large number 
of consecutive experiments (even though poor) are taken, the figures 
are in good accord with those given by the most perfect experiments 
such as the one quoted above (Table X). In the series of experiments 
made by Mr. John Zwick, in our laboratory, on less perfect samples, the 
mean value of the critical concentrations was obtained by eliminating the 
experiments which showed no minima at all, or minima the amplitude 
of which was inferior to 1 dyne. Thus the following mean values 
are obtained for the three critical concentrations; (45 series of 
experiments totalling 4,590 measurements). 1/750,000; 1/1,221,500; 
1/1,389,200. 



92 SURFACE EQUILIBRIA 



TABLE 
Sodium Oleate. 



Exper. No.: 


1 


2 


3 


4 


5 


6 


7 


8 


9 


10 


11 


12 


13 


14 


Concentration 


























S. 


T. in 


1: 1,000 


30.3 


29.0 


27.9 


27.5 


28.9 


33.0 


30.2 


29.9 


31.0 


29.2 


28.7 


29.4 


28.5 


33.4 


1: 5,000 


33.0 


35.0 


34.4 


35.5 


36.1 


39.2 


38.0 


38.0 


41.0 


32.0 


38.3 


36.1 


35.7 


37.4 


1: 10,000 


37.0 


36.5 


36.0 


39.0 


39.2 


42.0 


40.2 


40.3 


44.4 


40.5 


38.3 


39.8 


39.4 


40.0 


1: 50.000 


44.4 


44.0 


40.5 


43.0 


47.0 


47.5 


44.8 


45.3 


50.0 


44.6 


42.8 


43.5 


42.0 


43.8 


1: 100,000 


49.0 


47.0 


41.0 


49.0 


64.4 


69.8 


54.0 


53.0 


51.2 


48.0 


50.3 


53.0 


54.1 


47.0 


1: 200,000 


51.0 


58.0 


56.4 


60.3 


75.0 


76.2 


68.5 


67.9 


64.8 


59.4 


70.9 


74.4 


71.5 


68.0 


1 : 300,000 


69.0 


72.0 


71.6 


72.4 


75.4 


77.0 


76.4 


76.1 


76.2 


68.5 


74.9 


76.1 


74.8 


76.2 


1 : 400 000 


72.2 


72.0 


71.7 


72.9 


75.2 


77.0 


76.3 


76.1 


75.0 


74.8 


75.1 


76.1 


75.0 


76.2 


1 : 500,000 


74.0 


74.5 


74.7 


73.3 


73.2 


77.0 


76.6 


76.2 


76.4 


74.9 


75.1 


76.0 


74.9 


76.2 


1: 600,000 


74.6 


74.5 


74.0 


73.6 


75.4 


77.0 


76.3 


76.2 


76.4 


74.9 


75.1 


75.9 


75.0 


76.1 


1: 700,000 


74.6 


74.0 


74.2 


73.5 


75.4 


77.0 


76.4 


76.2 


76.4 


74.9 


75.2 


75.9 


75.1 


76.2 


1: 725,000 


74.7 


74.5 


74.4 


73.4 


75.4 


76.9 


7.64 


76.1 


76.4 


75.0 


75.0 


76.0 


74.9 


76.2 


1 : 730,000 


74.7 


74.5 


74.7 


73.7 


75.3 


77.0 


76.3 


76.2 


76.4 


75.0 


75.1 


76.0 


75.1 


76.0 


1 : 735,000 


74.8 


74.7 


74.6 


73.6 


75.3 


77.0 


76.3 


76.0 


76.4 


74.9 


73.2 


76.1 


75.0 


76.2 


1 : 740,000 


74.9 


74.7 


74.7 


73.4 


75.4 


76.9 


76.5 


76.2 


76.4 


74.9 


70.0 


76.1 


75.2 


76.2 


1: 745,000 


74.7 


74.7 


74.6 


73.6 


75.4 


76.9 


76.1 


76.2 


76.4 


75.0 


72.6 


75.9 


75.2 


70.0 


1: 750.000 


74.9 


74.6 


74.8 


73.4 


75.4 


77.0 


69.8 


75.1 


76.0 


58.0 


74.1 


75.9 


71.5 


76.2 


1: 755,000 


74.8 


74.8 


74.3 


72.6 


75.4 


77.0 


76.2 


71.4 


70.7 


71.0 


75.2 


76.1 


69.0 


76.1 


1: 760,000 


74.8 


74.8 


74.8 


73.4 


75.3 


77.0 


76.2 


68.2 


76.5 


75.1 


75.1 


76.1 


75.1 


76.1 


1: 765,000 


74.9 


74.8 


74.9 


73.5 


75.3 


77.0 


76.3 


68.7 


76.4 


73.6 


75.2 


75.9 


75.1 


76.1 


1: 770,000 


74.8 


74.6 


74.8 


73.2 


75.4 


76.9 


7.64 


76.2 


76.3 


75.0 


75.1 


76.2 


75.1 


76.1 


1: 775 000 


74.7 


74.7 


74.6 


73.5 


75.2 


76.9 


76.4 


76.1 


76.3 


75.0 


75.0 


76.1 


75.1 


76.1 


1: 800,000 


74.6 


74.7 


74,.7 
74.6 


73.7 


75.2 


76.9 


76.3 


76.2 


76.3 


75.0 


75.1 


76.2 


74.9 


76.1 


1: 900,000 


74.6 


74.8 


73.6 


75.3 


76.9 


76.4 


76.2 


76.4 


74.9 


75.1 


76.1 


75.1 


76.1 


1 : 1,000,000 


74.5 


74.8 


74.8 


73.6 


75.2 


76.9 


76.4 


76.2 


76.3 


74.9 


75.1 


76.3 


75.1 


76.0 


1: 1,100,000 


74.8 


74.8 


74.8 


73.5 


75.3 


76.9 


76.3 


76.3 


76.4 


75.0 


75.1 


76.3 


75.1 


76.0 


1: 1,200,000 


74.8 


74.8 


74.8 


73.4 


75.2 


76.9 


76.3 


76.1 


76.4 


75.0 


75.0 


76.2 


75.0 


76.0 


1: 1,205,000 


74.8 


74.8 


74.7 


73.4 


75.2 


76.9 


76.3 


76.2 


76.4 


74.9 


75.0 


76.1 


74.9 


76.0 


1: 1,210 000 


74.9 


74.7 


74.9 


73.3 


75.3 


76.9 


76.3 


76.2 


76.4 


74.9 


75.0 


75.9 


74.9 


76.2 


1: 1,215,000 


74.9 


74.6 


74.7 


74.0 


75.2 


76.9 


76.1 


76.2 


76.4 


74.9 


75.1 


76.1 


74.9 


76.0 


1: 1,220,000 


74.8 


74.6 


74.8 


73.7 


75.5 


76.9 


76.3 


76.2 


76.4 


74.9 


75.1 


76.1 


75.2 


76.0 


1: 1,225,000 


74.9 


74.6 


74.8 


74.0 


75.4 


77.0 


76.3 


75.0 


76.4 


72.7 


75.3 


76.1 


67.9 


76.2 


1: 1,230,000 


74.9 


74.7 


74.9 


74.0 


75.3 


77.0 


76.2 


76.1 


76.4 


68.4 


75.2 


76.1 


72.2 


76.2 


1: 1,240.000 


74.7 


74.6 


74.9 


73.9 


75.3 


77.0 


76.2 


76.1 


76.4 


68.8 


75.2 


, 75.9 


74.9 


76.2 


1: 1,250,000 


74.6 


74.7 


74.8 


73.9 


75.3 


77.0 


76.3 


76.2 


76.4 


75.0 


75.1 


76.0 


75.1 


76.2 


1: 1.300,000 


74.7 


74.8 


74.8 


73.8 


75.4 


76.9 


76.3 


76.2 


76.4 


74.9 


75.2 


76.0 


75.0 


76.2 


1 : 1,350,000 


74.6 


74.9 


74.9 


73.8 


75.3 


77.0 


76.3 


76.2 


76.4 


75.1 


75.1 


76.1 


75.2 


76.2 


1: 1,360,000 


74.8 


74.9 


74.9 


73.8 


75.4 


76.9 


76.2 


76.3 


76.4 


75.0 


75.1 


76.1 


75.1 


76.2 


1: 1,370,000 


74.8 


74.9 


74.8 


74.0 


75.3 


76.9 


76.2 


76.5 


76.4 


74.9 


75.4 


76.3 


75.3 


76.2 


1: 1,380,000 


74.8 


74.9 


74.9 


73.9 


75.4 


76.9 


73.2 


76.3 


76.4 


75.0 


75.3 


76.2 


75.1 


76.2 


1: 1,390,000 


74.9 


74.9 


74.9 


73.9 


75.2 


76.9 


76.5 


76.1 


76.4 


75.1 


75.1 


76.2 


75.1 


76.2 


1: 1,400,000 


74.9 


74.9 


75.0 


74.0 


75.2 


77.0 


76.5 


76.3 


76.4 


71.9 


75.1 


75.9 


75.3 


76.2 


1: 1,500,000 


74.9 


74.8 


74.7 


74.0 


75.2 


77.0 


76.5 


76.5 


76.5 


75.0 


75.2 


76.1 


75.1 


76.2 


1: 2,000,000 


74.9 


74.9 


75.0 


74.2 


75.1 


77.0 
2640 


76.5 
mts. 


76.5 


76.5 


74.9 


75.0 


76.1 


75.1 


76.2 



SODIUM OLEATE— DIMENSIONS OF THE MOLECULE 93 



XI. 1 

Static Surface Tension. 



15 


16 


17 


18 


19 


20 


21 


22 


23 


24 


25 


26 


27 


28 


29 


30 


Dynes. Cir 


i. 




























28.6 


30.0 


31.7 


30.1 


27.7 


28.7 


26.7 


27.7 


27.7 


27.8 


25.7 


28.1 


29.6 


29.9 


30.0 


29.7 


35.2 


36.5 


35.5 


32.8 


35.0 


35.2 


28.5 


35.6 


35.6 


35.3 


31.9 


35.3 


36.4 


36.6 


36.9 


36.2 


39.8 


39.6 


65.7 


43.0 


37.4 


37.8 


34.4 


39.7 


39.6 


36.7 


34.0 


37.6 


38.6 


40.0 


39.1 


38.0 


11.5 


45.0 


74.5 


46.9 


42.3 


44.1 


41.5 


47.6 


44.1 


41.7 


43.5 


45.4 


43.2 


45.1 


45.2 


42.1 


46.0 


52.6 


74.5 


47.6 


47.7 


45.4 


42.8 


48.1 


43.3 


42.8 


43.3 


48.6 


45.7 


46.1 


46.6 


45.5 


66.7 


68.1 


74.5 


62.2 


54.9 


51.5 


47.1 


64.5 


46.0 


53.7 


42.3 


51.5 


57.8 


54.6 


49.8 


51.4 


72.5 


74.4 


75.2 


74.8 


62.5 


68.1 


55.5 


71.6 


53.2 


68.7 


52.0 


60.0 


59.2 


59.6 


59.5 


61.3 


74.9 


74.4 


75.2 


76.0 


71.0 


68.6 


59.0 


73.4 


63.4 


72.2 


59.0 


70.1 


65.2 


73.1 


70.2 


62.9 


74.8 


74.5 


75.3 


76.0 


74.5 


73.4 


73.3 


73.3 


63.8 


73.3 


64.8 


67.3 


68.7 


74.0 


74.0 


66.3 


75.0 


74.4 


75.3 


75.9 


74.5 


74.4 


72.8 


73.1 


72.8 


73.2 


67.4 


73.0 


73.4 


74.5 


74.0 


72.2 


74.8 


74.5 


75.3 


76.0 


74.6 


74.2 


73.4 


73.0 


72.4 


73.1 


69.9 


73.0 


74.4 


74.7 


74.9 


73.5 


74.8 


74.5 


75.3 


76.1 


74.7 


74.3 


73.4 


71.0 


72.5 


73.3 


71.3 


72.9 


74.7 


73.2 


74.8 


74.5 


74.8 


74.6 


75.3 


76.1 


74.5 


74.3 


73.4 


73.2 


73.3 


73.2 


72.1 


72.7 


74.9 


74.8 


74.2 


68.1 


74.8 


74.5 


75.4 


76.0 


74.5 


74.3 


73.3 


73.3 


71.1 


73.2 


72.8 


73.0 


74.7 


74.8 


75.0 


74.6 


74.9 


74.6 


75.4 


76.1 


74.5 


74.4 


73.5 


73.2 


73.4 


73.2 


72.8 


72.9 


72.2 


72.7 


74. 1 


74.6 


74.0 


74.6 


75.3 


76.1 


74.5 


74.3 


73.3 


73.2 


73.4 


73.3 


72.7 


72.9 


73.2 


74.6 


1^.1 


74.4 


75.0 


74.6 


75.3 


76.1 


74.5 


74.4 


73.0 


73.2 


73.5 


73.3 


72.7 


72.8 


74.2 


74.8 


74.8 


70.9 


71.9 


74.6 


75.4 


76.0 


74.4 


74.4 


73.5 


73.5 


73.6 


73.2 


70.3 


72.9 


74.5 


74.6 


74.8 


72.3 


74.4 


74.7 


75.4 


76.1 


74.3 


74.4 


73.5 


73.2 


73.5 


73.3 


72.9 


72.9 


74.7 


74.6 


78.0 


74.6 


71.8 


74.7 


75.5 


75.9 


74.5 


74.4 


73.5 


73.0 


73.6 


73.5 


72.6 


69.8 


74.6 


74.6 


74.8 


74.0 


75.1 


74.5 


75.4 


76.0 


63.6 


74.4 


73.3 


73.3 


72.8 


73.3 


72.4 


73.0 


74.5 


74.6 


74.8 


74.7 


75.0 


74.7 


75.4 


76.0 


74.7 


74.4 


73.4 


73.2 


73.5 


73.3 


72.8 


72.4 


74.4 


74.7 


73.8 


74.6 


75.1 


74.7 


75.5 


75.9 


74.4 


74.4 


73.6 


73.1 


73.4 


73.4 


72.9 


73.0 


74.5 


74.5 


74.8 


74.6 


75.0 


74.7 


75.3 


76.0 


74.5 


74.4 


73.5 


73.2 


73.4 


73.5 


72.8 


72.9 


74.7 


74.7 


74.9 


74.4 


75.2 


74.7 


75.3 


75.9 


74.6 


74.4 


73.6 


73.3 


73.4 


73.5 


72.7 


72.8 


74.5 


74.7 


74.8 


74.7 


75.1 


74.7 


75.4 


76.0 


74.6 


74.4 


73.6 


73.2 


73.5 


73.3 


72.7 


72.9 


74.6 


74.7 


74.9 


73.9 


74.0 


74.7 


75.4 


76.0 


74.5 


74.4 


73.5 


73.2 


73.4 


73.3 


72.6 


73.0 


74.5 


74.7 


74.7 


74.6 


74.6 


74.6 


75.4 


75.9 


74.5 


74.4 


73.2 


73.2 


73.3 


73.3 


72.5 


73.0 


74.4 


74.6 


74.7 


74.6 


74.7 


74.6 


75.3 


76.0 


74.5 


74.4 


73.4 


73.2 


73.3 


73.1 


72.5 


66.5 


74.7 


74.7 


74.7 


74.5 


69.5 


74.6 


75.6 


76.0 


74.5 


74-0 


73.6 


50.7 


73.3 


73.3 


72.6 


72.8 


74.7 


74.7 


74.7 


74.6 


74.8 


74.5 


75.4 


76.0 


74.5 


74.4 


73.4 


73.3 


73.4 


73.4 


72.8 


72.7 


74.6 


74.8 


74.7 


74.7 


74.9 


74.5 


75.4 


75.8 


74.5 


74.3 


73.3 


73.2 


73.3 


73.1 


72.9 


73.0 


74.7 


74.6 


74.8 


74.5 


75.1 


74.4 


75.5 


75.8 


74.5 


74.4 


73.4 


73.5 


73.4 


73.3 . 


72.9 


72.8 


74.7 


74.6 


74.8 


74.5 


75.2 


74.4 


75.6 


76.0 


74.5 


74.4 


73.4 


73.2 


67.5 


73.3 


73.0 


69.4 


74.8 


74.6 


74.8 


74.5 


75.0 


74.4 


75.6 


75.9 


74.5 


74.4 


73.5 


73.2 


73.5 


73.3 


73.0 


72.8 


74.6 


74.5 


74.7 


74.7 


74.9 


74.5 


75.7 


75.9 


74.6 


74.4 


73.6 


73.2 


73.3 


73.2 


73.1 


73.0 


74.6 


74.5 


74.8 


74.7 


71.2 


74.5 


75.6 


75.9 


71.9 


74.4 


54.7 


73.3 


73.3 


73.4 


73.0 


73.0 


74.5 


74.5 


74.7 


74.7 


75.2 


74.4 


75.8 


76.1 


74.6 


74.2 


73.5 


73.3 


73.4 


69.5 


73.1 


73.0 


74.7 


74.6 


74.7 


74.7 


74.9 


74.5 


75.6 


76.0 


74.6 


74.2 


73.6 


73.3 


73.4 


73.5 


73.0 


72.9 


74.5 


74.8 


74.8 


74.7 


74.9 


74.5 


75.6 


76.1 


74.6 


74.3 


73.6 


73.5 


73.4 


73.4 


73.0 


72.9 


74.6 


74.6 


74.8 


74.7 


75.0 


74.5 


75.5 


70.9 


74.6 


74.4 


73.7 


73.3 


73.3 


73.4 


73.0 


72.8 


74.6 


74.5 


74.8 


74.7 


75.1 


74.6 


75.6 


76.1 


74.5 


74.5 


73.5 


73.3 


67.9 


73.4 


73.0 


72.8 


74.6 


74.9 


74.8 


74.7 


75.1 


74.3 


75.5 


75.7 


74.7 


74.2 


73.3 


73.2 


73.4 


73.4 


73.0 


72.9 


74.7 


74.8 


74.8 


74.7 


74.8 


74.4 






74.5 


74.5 


73.4 


73.2 


73.3 


73.5 


73.0 


72.8 


T4.6 




74.7 


74.6 



1 It will be observed that, although fairly constant throughout each vertical column, the 
figures vary from one column to the other, even when the high dilutions are reached. For 
instance, columns 1, 2 and 3 give a mean value of 74.8, from 1/735,000 down, while column 6 
gives 76.9 and column 11, 75.2. This is due to the fact that 4 different tensiometers were em- 
ployed at different time intervals, and that they had not been standardised in absolute units 
before use. However, this is immaterial as only the differences in S. T. were sought, and not 
the absolute values of the S. T. For the same reason, the measurements were made according to 
the simpler technique described on page 28 and not according to Klopsteg's technique. The same 
instrument was always used throughout one series of dilutions. 



94 SURFACE EQUILIBRIA 



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WO rH 



SODIUM OLEATE— DIMENSIONS OF THE MOLECULE 95 



t— 1 








X 


u 




H 


w 


< 


pq 


CO 


< 




H 


a 



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WU rHrHrHrH r-i rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH rH 



96 SURFACE EQUILIBRIA 

Considering that the lowest values of static surface tension usually 
occur at 1/750,000, 1/1,220,000, and 1/1,389,000; and, on the other 
hand, that the larger the number of measurements the smaller the 
discrepancy, the writer feels that they may be considered as the cor- 
rect values for sodium oleate. 

One hundred complete series of experiments were made. These 
represent about 8,800 measurements of surface tension. As a matter 
of fact, more than 10,000 were made, for when perfect samples were 
dealt with more than 44 dilutions were studied so as to determine 
the position of the minimum more accurately. Minima remote from the 
three critical concentrations were never observed ; in certain cases, 
however, (experiments 15 and 19 on the table) a minimum was ob- 
served around 1/1,350,000. This exception was probably due to a 
combination of vertical and horizontal molecules. 

The solutions which showed clear cut and important minima at or 
very, near the dilutions, 1/750,000, 1/1,220,000, 1/1,390,000, were 
always made from an initial solution of 1/1000, perfectly clear and 
showing no trace of opalescence. In this case the solution is a true 
solution with only a very small number of molecules aggregated as 
colloidal micellae. It wa sfound that certain samples of sodium oleate 
were absolutely incapable of yielding such solutions. The hydrogen 
ion concentration certainly plays a part in this effect, for the opalescent 
solutions may be cleared by a slight alkalinisation of the liquid. But 
this is not the only factor which intervenes since all the solutions were 
made at the same original pH and there was no means of foretelling 
whether they would be clear or of a colloidal appearance. Moreover, 
after being clarified with alkali, the solutions did not show marked 
minima. 

Consequently, the same values are obtained for the position of the 
three minima, whether the figures given by the perfect experiments 
(20 per cent) are chosen, or whether the mean values of all the poor 
experiments are calculated. The static value of the surface tension 
is in certain cases very low, which shows with what power extremely 
small quantities of substance can act on the surface tension of water. 
In experiment No. 22, Table XII, for instance, less than 1/610,000 
of a gram of sodium oleate lowers the surface tension of 2 cc. of 
water by as much as 23 dynes. 

A simple and logical explanation, therefore, of the three minima, 
is the polarised organisation at each minimum, of a single layer of 



SODIUM OLEATE— DIMENSIONS OF THE MOLECULE 97 

molecules in the surface layer. 5 ' The first minimum is due to the vertical 
orientation of the molecules ; the second, to their horizontal orientation, 
and the third, to a rotation of 90° of these molecules around their hori- 
zontal axis. It therefore becomes possible to calculate, as has been done 
for serum, the thickness of the monolayer corresponding to these three 
critical concentrations. This leads to three different dimensions for the 
molecule. The specific gravity of sodium oleate was found to be 0.821. 
The greatest care was taken in determining this value which coincides 
exactly with the value published in the Beilstein and the Landolt 
tables. Thus the three dimensions of the volume occupied in space 
by one molecule of sodium oleate (Ci 7 H 33 COONa) are found to be: 
(Fig. 39) 

12.30 X 10- 8 cm. 
7.56 X lO" 8 cm. 
6.64 X lO" 8 cm. 




CH == 



/ 


/ 


CH 2 


CH, 


\ 


s 


CH 2 


CH 2 


/ 


/ 


CH 2 


CH 2 


\ 


\ 


CH 2 


CH 2 


/ 


/ 


CH 2 


CH 2 


\ 


\ 


CH 2 


CH 2 


/ 


/ 


CH 2 


CH 2 


N. 


S 


CH, 


C v°. 


/ 


N. 


H 


c 



7.56.10" 8 , 



Na 



/ 



Fig. 39. — Space occupied by a single molecule of sodium oleate in a monolayer. 
These dimensions seem to point to a folding of the chain around the double 
bond. 

The length of the molecule of oleic acid (C 17 H 33 COOH) found by 
Langmuir is 11.2 X 10~ 8 cm. He obtains a value of what he terms 
the mean diameter by extracting the square root of the mean area 
occupied by one molecule. This is equal to 6.8 X 10~ 8 cm. The 
method used by Devaux and Langmuir did not enable them to ob- 
tain an idea of the shape of the space occupied by the molecule of the 



•The writer is aware of the fact that this interpretation does not tally with 
some of the accepted adsorption theories. However, the quantitative consequences 
resulting from this hypothesis, which will now be dealt with, are so striking 
that it seems impossible not to take it into serious consideration. 



98 SURFACE EQUILIBRIA 

fatty acid in a monolayer. Their experiments did not indicate the 
existence of a monolayer of horizontal molecules of oleic acid. The 
mean area occupied by a single molecule was obtained by measuring 
the total surface of the liquid covered by the monolayer which was 
then divided by the number of molecules present. The square root 
of this figure expresses the length of the sides of the plane section, 
assuming that this section is a perfect square. The figure 6.8 angstroms 
for this dimension is consequently based on an assumption which never- 
theless allowed Langmuir to state that molecules were not spherical. 
A brief summary of the works on which Langmuir's papers are based 
may not be without interest for the reader. 

The remarkable, fundamental study of Lord Rayleigh, 6 Pockels, 7 
and Devaux, 8 opened a new field to physicists for the measurement 
of the dimension of certain molecules. They were followed by those 
of Marcelin 9 and of Langmuir 10 who brought the subject into the 
limelight in a paper in which Devaux' s experiments are reproduced 
and all his assumptions and results confirmed. Devaux extended the 
work of Miss Pockels and of Lord Rayleigh and developed experi- 
mental methods for the study of oil films which Langmuir quotes as 
being "beautiful in their simplicity and remarkable in the clearness 
with which they demonstrate the existence of monomolecular oil films." 
The experiments and calculations by which Devaux and Langmuir 
reached the dimensions of the molecules of oils, fats, or waxes are 
very simple A known weight of the rubstance is dissolved in benzene. 
A drop of this solution is placed ov water. It spreads, and the 
solvent (benzene) evaporates and leaves the monolayer of oil. The 
area covered by this layer is measured and, as the weight of the drop 
is known, the weight of oil divided by the total area gives its weight 
by square cm. ; hence, when the specific gravity of the substance is 

"Lord Rayleigh. Phil. Mag. 1899, XLVIII, p. 331. 

7 A. Pockels. Nature, 1891, XLIII, p. 437. 
8 Professor Devaux published a large number of papers between 1903 and 1914. 
A review of his work appeared in the Annual Report of the Smithsonian 
Institute for 1913, p. 261. Subsequent papers are: Devaux, Soc. Franc. Phys. 
1914, LV, p. 3 ; LVII, p. 3, and quite recently, J. de Phys. et Radium, 1923, IV, 
series 6, p. 293. 

9 A. Marcelin. Ann. de Phys. 1914, I, p. 19. 

10 1. Langmuir, J. Am. Chem. Soc. 1917, XXXIX, p. 1848. Besides this fun- 
damental paper on the structure of surfaces, the splendid work of Prof. Harkins 
and his collaborators on mono- and poly-molecular films has recently thrown 
much light on the question. (Proc. Nl. Ac. of Sc. 1925, XI, pp. 631-637 and 
previous papers). The importance of his contributions to our knowledge of 
surface films is considerable. The work of Adam (Proc. Roy. Soc. 1921, A, CL, 
452, and later papers) is also of great importance. 



SODIUM OLEATE— DIMENSIONS OF THE MOLECULE 99 

known the thickness of the layer is readily obtained. Obviously, this 
method rests entirely on the possibility of obtaining a monolayer, on 
the experimental evidence of its existence and on the method devised 
to measure its area. The problem was relatively simple as long as 
non-soluble substances were used, since all the molecules remained 
at the surface of the water. But when soluble substances were dealt 
with the problem was totally different and a new criterion of the 
existence of monolayers was sought and found in the minima of static 
surface tension. 

From the dimension obtained for sodium oleate it is clear that the 
horizontal section of this molecule is not a perfect square but a 
rectangle, measuring : 7.56 X 6.64 angstroms. The surface of this 
rectangle is 50.2 X 10~ 16 cm. 2 X1 , while the surface of the horizontal 
section of the oleic acid molecule is, according to Langmuir, 46 X 10 -16 
cm. 2 The difference of 4.2 X 10~ 16 cm. 2 may be due to the presence 
at the end of the molecule of the large sodium atom which is also 
responsible for the difference in the length of the two molecules, i.e. 
1.1 X 10" 8 cm. If the atoms were disposed in a straight line the 
difference would be greater and both molecules would be longer, but 
it is known that an angle of approximately 109° exists between the 
valences of the carbon atom. Consequently, in a carbon chain, the 
atoms are disposed in zig-zag fashion and the increase in length of 1.1 

11 E. L. Griffin (J. Am. Chem. Soc. 1923, XLV, p. 1648, has determined 
this surface by a different method also based on adsorption. The value he gives 
is 48.27 X lO" 10 . This value differs from ours by 1.93 X 10" 16 and is larger than 
that of Langmuir by 2.27 X 10" 16 . But this value, 48.27 X lO" 18 is obtained by 
taking the mean of 18 experiments, which gave figures ranging between 44 and 
52 X 10~ 16 cm 2 . Moreover, this method, though very ingenious, involves the esti- 
mation of the adsorbing surface of kerosene drops of different dimensions. This 
introduces an element of approximation difficult to estimate, whence the wide 
fluctuation in his values. 

W. D. Harkins and Henrietta Zollman have quite recently published (J. Am. 
Chem. Soc. 1926, XLVIII, p. 69) the value 47 X lO" 16 for the same surface. 
(Adsorption at the interface, Sol-Benzene.) It will be shown later that there is 
strong evidence in favour of the area resulting from the figures obtained from 
our calculations, i.e., 50.2 X 10" 18 . At any rate, the satisfactory accord of these 
three values demonstrates beyond a doubt that the structure of sodium oleate 
conforms to the Fig. 39. 

Marcelin has also recently published (Ann. de Phys. 1925, IV, p. 459) figures 
which differ entirely from those published by Langmuir as regards the length 
of the oleic acid molecule. His experiments lead him to admit for this length the 
value 22.2 X 10~ 8 cm. which indicates that he dealt with an "unfolded" molecule. 

On the other hand, Langmuir's experiments clearly showed that the "folded" 
form could also exist at the surface of water. The experiments of A. Muller 
and G. Shearer (Trans. Chem. Soc. 1923, CXXIII, p. 3156) and of L. de Broglie 
and J. J. Prillat (C. R. Acad. 1925, CLXXX, p. 1329, 1338 & 1485) point, for the 
length of the oleic acid molecule, to a value between 18 and 27 X 10" 8 cm. by 
the X-ray analysis method. 



100 SURFACE EQUILIBRIA 

angstrom represents the projection on the vertical axis of the molecule 
of the distance between the last oxygen atom and the sodium atom. 12 

Calculation of the Avogadro Constant N: 

Assuming that the space occupied by the molecule of sodium oleate 
is a rectangular parallelopiped, we can now calculate its volume with the 
aid of the above dimensions. It is equal to 617.44 X 10~ 24 cc. The 
density of the dried substance being 0.821, the mass of the molecule is 
506.91 X 10~ 24 gm. By dividing the molecular weight 304.35 by 
506.91 X 10~ 24 , we should, according to the very definition, find a value 
for the constant N of Avogadro. This calculation is of crucial impor- 
tance; for the invalidation or the confirmation of our hypothesis and 
of all our experiments will depend on whether the value obtained is 
in accord with that of Millikan, which is admittedly the best. Now 
the value we find is : 

N = 6.004 X 10 23 
and Millikan's figure is : 

N = 6.062 X 10 23 

The difference is 0.058 X 10 23 , or less than one per cent. It is there- 
fore probable that the dimensions found for the molecule of sodium 
oleate are exact to the second decimal point and that all our hypotheses 
were well founded: (1) that the absolute minima of the static sur- 
face tension are due to the organisation of molecules in its polarised 
monolayer; (2) that the molecule of sodium oleate, in particular, can 
orient itself by rotation in three different ways in the surface layer 
of water; (3) that the shape of the space occupied by such a mole- 
cule in the afore-mentioned conditions is a rectangular parallelopiped. 
The monolayer is perfectly homogeneous and can therefore be likened 
to a two dimensional crystal in which the molecules lose their indi- 
viduality. Hence the density may be considered as a specific property 
of all the space occupied by the substance, and in particular of all the 
space occupied by the above defined parallelopiped. The notion of 
density can thus be applied to an individual molecule and assumes a very 
clear significance. 

An important consequence of these conclusions is that at low con- 
centrations the great majority of molecules are free and are not grouped 
as micellae. The colloidality of sodium oleate thus ceases under cer- 
tain conditions. We have already pointed out that only clear solu- 

12 It is to be observed that these figures lead to a smaller value for the radius 
of the sodium atom than that generally accepted and derived from X-ray analysis, 
i.e., 1,775 angstrom. 



SODIUM OLEATE— DIMENSIONS OF THE MOLECULE 101 

tions gave clear cut minima. Whenever there are micellar aggrega- 
tions it becomes impossible for the molecules to orient themselves 
individually in a monolayer. It is hard to define the conditions under 
which a true solution of sodium oleate can be obtained. By a true 
solution we mean a solution in which the molecules are separated, 
without reference to their state of ionisation. Later on we shall see that 
there are solutions of so-called colloids in which minima are always 
produced; which would lead to the supposition that the colloidal state, 
defined as a result of the aggregation of molecules, is in no wise a 
specific character of such substances. 

Assuming that the molecules of sodium oleate are ionised and that 
we have on one side the oleic ions and on the other the Na ions, it 
can be supposed that the oleic ions are adsorbed separately and that 
the free Na ions are attracted to the oleic layer which is oppositely 
charged. The recombination could thus take place in the adsorbed layer 
itself. 

Discussion of the Errors : 

If the above mentioned experiments are considered as a method of 
calculating the constant N, it is of interest to know the degree of 
approximation obtained by examining the causes of error. These errors 
are relatively small, as the absolute values of surface tension do not 
come into play. Only measurements of weight, volume and surface, 
which are simple and do not involve important errors, intervene in 
the calculations. Outside of these determinations the method is only 
dependent on the exactitude with which the positions of the minima can 
be determined. We have seen (page 96) that the results are the same, 
whether based on perfect experiments in which the sodium oleate exists 
in true solution and in which the minima are very important, or whether 
based on the mean value of the concentrations at which minima have 
been produced in large series of measurements. The critical concen- 
trations are 1/750,000, 1/1,220,000, 1/1,390,000. As the differences 
between the good experiments and the mean values of all the experi- 
ments do not amount to more than 0.2 per cent, it can be stated that 
the minima are clearly defined. 

If it be admitted that the molecular weight of sodium oleate is exact, 
or if we choose to neglect the possible error which is certainly very 
small, in the atomic weights of its constituents, it may be stated that 
the error in the value of N is dependent solely on the errors involved 
in the determination of the mass of a single molecule of sodium ole- 



102 SURFACE EQUILIBRIA 

ate. This mass, as calculated from our measurements, may be expressed 
by the formula : 

m 8 . d . C 2 . Q, (l) 

A 3 . 5- K } 

as one of the linear dimensions is equal to 

T m . C 

L_ AT8~ 
M= mass of one molecule of substance (to be computed), 
m = mass of mixture in watch glass, always assumed at 22° C. 
= 2 X 0.9979 (temperature correction). This is true if the 
density of water is 1 gm./cm. 3 , and the concentration of 
the substance very small. 
A = area of adsorbing surface (total surface of water in con- 
tact with air and glass. 
5 = specific gravity of substance in solution. 
Ci, C 2 , C 3 = critical concentrations at which the minima are observed. 

The various values of the critical concentrations d, C 2 , C 3 , corre- 
sponding to each of the three minima obtained in the course of 23 
series of perfect experiments, exhibited a degree of consistency which 
may be described by saying that the most extreme value for any of 
these three points has in no case differed from the mean obtained 
from 103 series of experiments by more than 0.2 per cent. 

It may be assumed that the error in the determination of the area 
of the surface of adsorption does not exceed 0.2 per cent. 

Since the determinations were made at constant temperature (22° C.) 
and with concentrations not greater than 1/750,000, or 0.000,001,333 
gram per cc. of water, it may safely be assumed that the error in the 
value of M used in the calculation is the same as the error in measur- 
ing the volume of the liquid used, which is not more than 0.1 per cent. 

The possible error in M may be estimated, therefore, as follows : 

Factor Assumed Error 

m 0.1 per cent 

C 0.2 " " 

A 0.2 " " 

and by reference to equation (1) 

Factor Assumed Error 

m 0.3 per cent 

Ci, C 2) C 3 0.6 " " 

A 0.6 " " 

1.5 per cent 



SODIUM OLEATE— DIMENSIONS OF THE MOLECULE 103 

This error of 1.5 per cent can only occur if all the several errors — 
nine in number — happen to have their maximum value and are of the 
same sign, which is obviously highly improbable. A calculation of 
the probable error, on the assumption that each of the individual errors 
has its maximum value but that it may with equal probability be 
+ or — , gives the value of 0.13 per cent. To this value must be 
added, of course with due respect to sign, twice the value of any error 
in the value of 5. The various available values of 8 are identical, and 
expressed as accurate to within 0.1 per cent (Beilstein). 

It is believed, therefore, that the value of TV calculated above is 
correct within 0.15 per cent, i.e. 

N = 6.004 ± 0.009 X 10 23 

Nevertheless it is not our intention to claim for this value a greater 
accuracy than that of the figure published by Millikan, as a result 
of his admirable and exact measurement of the charge of a single 
electron. The difference of 1 per cent between the two figures indi- 
cates that there is probably another cause of error in our experiments, 
or that we have underestimated those that we mention. The interest 
of the figure obtained by the above described method, lies chiefly in 
the fact that it confirms our hypothesis concerning the monolayers and 
that it is derived from the only method based on the very definition 
of the Avogadro Constant. To our knowledge it is the most direct 
and simple method yet devised. 13 

13 It may not be without interest to recall the principal determinations of the 
Avogadro Constant, as compared with ours. 

Lorentz Radiation of a black body JV = 7.7 X 10 23 

Planck " " " " " 6.02 

Svedberg Brownian Movement of Colloidal "Par- 
ticles " 6.2 

Brillouin Brownian Movement of Colloidal Par- 
ticles " 6.9 

Perrin Angular Displacement of Colloidal 

Particles " 6.5 

Perrin Brownian Movement of Colloidal Par- 
ticles " 6.85 

Westgren Variation in the Distribution of Col- 
loidal Particles " 6.09 

Fletcher Fall of Oil Drops in Air " 6.03 

King Diffraction of Solar Light " 6.2 

Pacini " " " " " 5.7 

Curie Alpha Particles of Polonium " 6.5 " 

Rutherford Kinetic Energy of Alpha Particles... " 6.2 " 

Rutherford Charge of Alpha Particles " 6.0 

Boltwood Helium produced by Radium " 6.3 " 

Millikan Charge of the Electron " 6.062 

Lecomte du Noiiy Surface Tension " 6.00 " 



104 SURFACE EQUILIBRIA 

The aspect of sodium chloride crystals formed after evaporation in 
the watch glasses when a saline solution is used instead of water, is 
recorded in Chapter 7, where it will be seen that at the critical 
concentrations the appearance of the crystals is different and quite 
characteristic. 



Chapter 5. 
Study of the Egg Albumin Molecule. 

The problem is different in the case of proteins in general and egg 
albumin in particular. There are indeed many points in common, but 
also marked dissimilarities. Egg albumin is a well denned protein 
which can be obtained in the crystalline state and therefore pure. Like 
sodium oleate its solutions show minima of static surface tension. 
Although its chemical constitution is known, there has been wide 
discussion as to its molecular weight, as a result of the consider- 
able difficulty encountered when it is attempted to determine this 
directly by means of the customary methods, osmotic pressure, freez- 
ing point, etc. The chemical constitution of egg albumin is given by 
Osborne * as : 



5275. H = 7.10. N = 15.51. 



1.616. = 23.024. 



As stated above, egg albumin is a stable and well defined compound. 
Repeated precipitations under properly controlled conditions do not 
affect the shape nor the composition of its crystals in any way. 

In most proteins, sulphur exists in combination, in the form of 
cysteine; perhaps also of cystine, which is the result of the oxidation 
of two molecules of cysteine. 



H 

I 
HC — SH 



HS 



H 

I 
C 



H 



H H 

I I 

HC — S . . S . . — C- 



H 



HCNH 2 + O + 

I 

COOH 

Cysteine 



HCNH 2 = HCNH 2 

I I 

COOH COOH 

cysteine 



HCNH 2 + H 2 

I 
COOH 



cystine 



Thus if there is one molecule of cystine in one molecule of protein 
there must be two atoms of sulphur in each molecule of this protein. 
The molecular weight of two atoms of sulphur is 64, consequently 

1 T. B. Osborne. J. Am. Chem. Soc. 1902, XXIV, p. 160. 

105 



106 SURFACE EQUILIBRIA 

the molecular weight of a protein will be at least 6400, if it contains 
1% of sulphur. If it contains 0.5% of sulphur its molecular weight 
becomes 12800. Osborne has established the empirical formula and 
calculated the possible molecular weights of a certain number of pro- 
teins by assuming the presence of at least two atoms of sulphur in 
each molecule. 2 The formula which he gives for egg albumin is : 

^696 -tj-1125 -IN 175 ^8 ^220* 

The molecular weight would be 15703. 3 It is evident that if egg albumin 
is a chemical entity its molecular weight must be very high and may 
be a multiple of the above figure. Assuming that this formula is cor- 
rect, the problem then consists in determining the coefficient by which 
15703 must be multiplied. So far only two direct determinations of the 
molecular weight of egg albumin are available, that of Sorensen 4 and 
that of Cohn, Hendry and Prentiss. 5 Sorensen with a method based on 
the measurement of osmotic pressure finds 34000, and Cohn and his 
co-workers, using an electrolytic method, find 33800. The order of 
magnitude of these figures struck some authorities as being so amazingly 
high that they did not hesitate to qualify them as "absurd." 6 But the 
value found by Cohn, based on an entirely different method, which 
happens to be in excellent accord with that of Sorensen, gives great 
weight to these figures. They indicate that the coefficient of the formula 
proposed by Osborne should be 2. Indeed Osborne's molecular weight 
multiplied by 2 = 31,406. The difference is less than 8 per cent. 

An attempt to determine this coefficient by the tensiometric method 
has been made in the following way. The albumin used, prepared 
in our laboratory by Dr. L. E. Baker, 7 was recrystallised three times 
and dialysed for seven days. The operations were carried on with 
sterile technique throughout. Solutions at pH 4.8 and 7.6 were prin- 
cipally studied. Figures 40 to 43 express the result of 26 series of 
consecutive experiments. Figures 44 and 45 show that no minima were 
observed at concentrations below 1/250,000 or above 1/70,000. In 

2 A. P. Mathews, Physiological Chemistry, N. Y. 1915. 

3 There are other determinations of the probable constitution of egg albumin. 
Among them that of A. Gautier (quoted by Lambling, Precis de Chimie Bio- 
logique, Paris), who gives C250 LU9 N 47 8 S 3 ; molecular weight, 5739. These 
figures are not even proportional to those of Osborne. 

4 S. P. L. Sorensen. C. R. Trav. Lab. Carlsberg, 1915-17, XII. 

B E. J. Cohn, J. L. Hendry, A. M. Prentiss. J. Biol. Chem. 1925, LXIII, 
p. 721. 

e H. Vigernon. Precis de Chimie Physique, Paris; Masson, 1924, p. 109. 
7 M. Heidelberger, An Advanced Laboratory Manual of Organic Chemistry ; 



STUDY OF THE EGG ALBUMIN MOLECULE 



107 



Dynes eq q alftamin 

70 
69 
68 
67 
66 



C 
o 

in 

2 70 

69 

68 



I 

§73 

en 72 
71 
70 
69 
68 



73 

72 
71 
70 
69 
68 

72 
71 
70 
69 
68 
67 
1/70,000 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 

Dilation 























































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:pl 






































































































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mi 




























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r 


























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H4 


o 




















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— ' — i-^ 4 














































f 


V £> 


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u 




























































































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v, 


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Fig. 40. 



108 



SURFACE EQUILIBRIA 



Dynes 
J 73 
72 
71 
70 
69 
68 
67 

72 
71 
70 
69 
68 
67 
66 
65 
64 
63 
62 

r 68 
o 67 
£ 66 
g 65 
** 64 
g 63 
£62 
% 61 
<n 60 
59 

66 

65 
64 
63 
62 
61 
60 
59 
58 
57 
56 

68 
67 
66 
65 
64 
63 
62 



> t:$ albumin 






-I- ^3 




_, =t z 






Exp. 10 , . 


-"^ 


"---^ ^""N. Z 1 ^^,^7 




~pH 4.8 N ^ 






^--^ 




-^d- 




^—^ ^ 


7V 


7 




r^ 


«**£— ^- J 1 '^ 


2 IT 


r}£L4iL_ A 7 J 7 




Vl H J 




st t 




L , . 








Expl2 T T 




~% ^""S 




3 t 4 7 


V- 


- A-- -H X ■/ 


\ 


X A ^ 


V 7A -n 


JDtL4i5 7 


X - 74 7^ 




4 t ' I V2 


^r- 


4- 7 ^ 




t -,£ t3 




A^ - 17 




Af 








7^ 3 




- W A ^ t 




t\ ^ A \ t 




4- X- Z ^ V7 




A AZ ^Z 


/ " r — "\ 


; 


5E 13 z_v 7 ^ 


t 


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_i 


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AZ 






"Z"^ Z 




7 ^ ' 




Z- 




^5 7 


Exp.^4 / \_^ 


^ / i 


^ N -,*- 7^ 




nH7i \ /N / 




N ^Z ^ 





1/70,000 80 90 



100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 
Dilution 



Fig. 41. 



STUDY OF THE EGG ALBUMIN MOLECULE 



109 



Dynes EQg albumin 

60 
59 
58 
57 
56 
55 
54 



'en 64 
g 63 

g> 72 

zi 60 

* 68 

67 



65 



* 



7^^^ 


s £5^x 75 v "^s; 


Z \./\/ l. 2! v 


jpfcLIf ^^ X ^z> _7 \ 




\ i 


_,^_ -Ht- 


-^5 A 


~ -^ _ ^v ■ 7 V- L V 


7- ^^^Y zr c \7 t 


gc^ifi t v t ^ i _p^ 


^C 7 X t 


_>: Z X '■ - 4 


N / \ 


4]fcLZ£:XZ . xz it 


-/X -^*- 


it ^ ^4 -^ ZS 


7 V 7 ZY7 X 


^teP- f < ^ -J- v-t K ^ 


A y'^-* \i ^ - ^ 




^ ^ i 


nH 7fi 


± A 'IT 


-v 4 


- ^ r ^ 




^ ^ ^ ^ = " 


^ ,z ^ z 


|fcl8_^ ^/__ 


-CH-76 - 




^/ 


-^S -^ 


7 z ^ ^ 




y'^'^V -^ 


y""\-^ ^-z - + 


Eip.19^/ 




pH Y.a A 


-,^V n 


/ \ '"A 


^ 17 l. Z_ \_ 


Exp£C .._ .. « — , / J V \ 


^-^-^ Z S 7 ^r ^ 


_pH_lf ^. _J V t 


t az \ — ^ 


^^ 



70,000 80 



90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 
Dilution 



Fig. 42. 



110 



SURFACE EQUILIBRIA 



Dynes 

71 
70 
69 
68 
67 
66 
65 
64 
63 
62 



Egg Albumin 



g 

en 
C 

& 67 



en 66 
65 

64 
63 
62 
61 
60 

66 
65 
64 
63 
62 

72 
71 
70 
69 

68 

67 





^ 




-— - — ^- -7 




X -7- 




A 7- 


^ — \ 1 


L. J 


tXpE. ^ \ j 


X L 


-7 v Z v- z 


4- -^ z 


Z \ j. \J? 




nH IB \ / 




' \ / 






-w- 




A 




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STUDY OF THE EGG ALBUMIN MOLECULE 



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STUDY OF THE EGG ALBUMIN MOLECULE 



113 



Figure 46 the frequency of the occurrence of the minima at different 
dilutions was plotted as ordinates. This chart facilitates the understand- 
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place, three principal groups of minima are to be observed. Their mean 
values correspond to the concentrations: 1/95,000 (first group), 
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Fig. 46. — Frequency of occurrence of minima. 



is 1/240,000. Each of these groups may correspond to one of the 
dimensions of the space occupied by the molecule, or one of these 
groups may be eliminated as due to a bimolecular layer and not to a 
monolayer. This seems to be the case for the first group, the mean 
concentration of which happens to be almost exactly double that of 
the third. To every individual minimum of the third group there 
corresponds a minimum at twice the concentration. Hence we may 
provisionally eliminate the first group. The frequent recurrence of 
the second group and in particular of the minima at or around 
1/140,000 indicates the existence of a privileged axis of orientation 
which we may term the "length." The third group would correspond 

8 Lecomte du Noiiy. J. of Biol. Chem. 1925, LXIV, p. 604. 



114 SURFACE EQUILIBRIA 

to the thickness or width of the molecule, and the fourth group could, 
perhaps, be the third dimension, unless it were simply due to experi- 
mental errors. We shall not consider the hypothesis which would consist 
in assuming that each individual minimum corresponds to one of the 
dimensions of the molecule, which would thus resemble a prism with 
a polygonal base ; for, even were it true, the error introduced by con- 
sidering only the mean values would be small as compared to the ex- 
perimental errors involved in the estimation of the volume. It may 
be noted that Figure 46 seems to indicate that the third group (between 
1/180,000 and 1/220,000 for instance) is decidedly less well defined 
than the second (between 1/130,000 and 1/150,000). This, however, 
is not the case, for it may be seen in the figure that the difference be- 
tween the thicknesses of the extreme monolayers of the second group is 
5.9 angstroms and that between those of the third group 4.6 angstroms 
(up to 1/210,000), and 5.8 angstroms up to 1/220,000. 

There is no doubt that the large molecule of albumin with its numer- 
ous side chains cannot orient itself as easily as does the simple mole- 
cule of sodium oleate. The momentum of the forces which tend to 
orient it horizontally is probably very weak, and the spreading of the 
minima over a relatively large range of concentrations may be due 
partly to combinations of differently oriented molecules. If this be 
1/240,000, the relative frequency of each of the individual minima 
most frequently observed without even introducing mean values. 

The volume and the mass of the molecule can therefore be computed 
in three different ways : 

(1) By admitting three dimensions, determined by the mean values 
of the minima around the concentrations 1/140,000, 1/190,000, and 
1/240,000; the relative frequency of each of the individual minima 
being taken into account in the calculations. The specific gravity of 
albumin being 1.295, the dimensions are found to be 42.0 X 30.3 X 
25.2 angstroms = 32080 cubic angstroms or 32.08 X 10" 21 cc. Mass = 
41.55 X 10 -21 gms. Molecular weight, 24,900 (taking for N the value 
of 6.06 X 10 23 ). This value is evidently a lower limit. 

(2) By admitting that the shape of the space occupied by the mole- 
cule is a prism of square base 42 angstroms high, the base being de- 
termined by the mean of all the minima between 1/180,000 and 
1/250,000, i.e. 28.6 angstroms. We thus obtain for the mass the 
value 44.5 X 10 -21 gms. and for the molecular weight 27,000. 

(3) By admitting that the only minima resulting from the organisa- 
tion of a polarised layer of molecules are those which are more fre- 



STUDY OF THE EGG ALBUMIN MOLECULE 115 

quently observed and that the less frequent minima are due to experi- 
mental errors or to imperfect organisations of the molecules. In other 
words, by eliminating all minima except that at 1/140,000 and that 
at 1/190,000, we obtain for the length of the molecule 41.7 angstroms, 
for the thickness (square base) 30.8 angstroms, volume = 39.60 X 10~ 21 
cc, mass = 51.30 X 10 -21 gms. Molecular weight, 30,800. This value 
may be considered as the upper limit obtainable by our experiments. 

We are personally inclined to think that this third interpretation 
is probably the correct one. Nearly 80 per cent of the measurements 
in our experiments showed the existence of a minimum at or around 
1/140,000 (between 1/135,000 and 1/145,000) ; more than 50 per cent 
showed a minimum at or around 1/190,000. The other minima appear 
to be due to more or less probable and stable combinations of horizontal 
and vertical molecules. This view is supported by the probability that 
the momentum of orientation of the large and complex molecule of egg 
albumin may be very weak. The molecular weight thus obtained 
differs by about 2 per cent from Csborne's figure multiplied by 2. 

Here again experiments point to the factor 2 as being correct and 
it is remarkable that three such different methods as Sorensen's, Cohn's 
and our own, should agree to within 10 per cent. Obviously if the first 
group of minima is considered as being due not to a double layer but to 
a monolayer corresponding to one molecular dimension, the values 
found will all have to be multiplied by 2 and a figure near 60,000 will 
be obtained for the molecular weight. This confirms the hypothesis 
made at the beginning with respect to these minima. 

The correctness of the figures thus experimentally found for the 
dimensions of the egg albumin molecule, evidently depends upon two 
main factors. First the legitimacy of our interpretation of the minima 
as due to an organised monolayer, which seems to be established by 
the experiments made with sodium oleate. The second factor may 
be expressed in the following manner: is it peimissible to apply the 
value of the specific gravity established for a crystal to an organised 
homogeneous monolayer or to an isolated molecule in this monolayer? 
This problem had already arisen in connection with sodium oleate ; 
but although our hypothesis in the latter case was confirmed, it did 
not follow a priori that such would be the case for other substances 
and especially for the huge and tremendously complicated molecule 
of egg albumin. Let us suppose indeed that in certain cases, at cer- 
tain concentrations, interpenetrations of molecules occur in such a way 
that the real thickness of the monolayer remains unchanged. This 



116 



SURFACE EQUILIBRIA 



new arrangement might determine a minimum of the surface tension. 
In this case our calculation, based on the concentration and on a con- 
stant value for the density, would yield a different figure for the thick- 
ness and it would appear as if the density were different in the two 

Imaginary cross- section of a molecule 




J Phantom; 
j shape of • 
| molecules • 
• AandC ! 



Fig. 47. — Imaginary cross-section of molecules, showing three possible arrange- 
ments in a polarized monolayer. In the first row, A, as well as in the third 
row, C, the molecules do not interpenetrate each other, so that the "phantom 
cross-section" of each individual molecule, when surrounded by others, is a 
square. The "phantom shape" of such a molecule is a prism with a square 
base. In the second row, B, the molecules interpenetrate each other, so 
that 5 occupy the same volume as 4 of- the first and third row. The square 
"phantom cross-section" does no longer exist, and the notion of specific gravity 
as characterising the property of the "phantom shape" disappears. The 
apparent specific gravities in both cases are in the same ratio as 4 to 5. 

cases. (Fig. 47.) As it is logical to suppose that the density of the 
crystal, 1.295, corresponds to the most densely packed organisations 
of molecules, it is probable that the calculated volume of the mole- 
cule would be inferior to the real volume and consequently the molecular 
weight too small. 

There may be a way of ascertaining whether this is the case, by 



STUDY OF THE EGG ALBUMIN MOLECULE 



117 



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118 SURFACE EQUILIBRIA 

utilising" some of the values obtained by Langmuir for the dimensions 
of a number of well known organic compounds. (Table XIV) 
Columns III, VI and VII have been added to Langmuir's table. The 
figures in column VII are the quotients of the corresponding figures 
of column VI (volume of the molecule) by those of column III 
(number of carbon atoms). The values of column VII, therefore, 
express the volume occupied in the molecule by one atom of carbon 
surrounded by its satellites H and O. This volume is evidently arbi- 
trary, nevertheless it will be seen that in all cases it is near 30 cubic 
angstroms. The mean value for the eight first substances is 29.7. 
If we accept the formula proposed by Osborne and the coefficient 2, 
the following figures are obtained when the same calculation is made 
for egg albumin. Number of carbon atoms 1392 ; volume of the mole- 
cule 39600 cubic angstroms ; volume occupied by 1 carbon atom 28.4. 
This figure is slightly below the mean value of Langmuir's data. 
If the volume of the molecule be deduced from the molecular weight 
given by Sorensen (34,000), we find 43700 cubic angstroms, and the 
volume of the carbon atom, as defined above, will be 31.4 cubic ang- 
stroms. It thus seems safe to conclude provisionally that the notion 
of density, as used in our calculations, applies to the molecule of 
egg albumin, and that the highest values obtained by our method are 
more likely to be correct than the lower values. Even when the 
highest value is accepted (39600 X 10^ 24 cc), the figure obtained for 
the volume occupied by a carbon atom is rather low. One of the 
conclusions from the foregoing observations is that egg albumin mole- 
cules do not interpenetrate, or, at any rate, not to such an extent as to 
cause any important error in our calculations. 

It appears then as though this molecule occupies in space a prismatic 
volume with a square base, 41.7 X 10~ 8 cm. high by 30.8 X 10" 8 cm. 
wide, at least. Sorensen's value would require the same height, and 
a length of the side of the square base equal to 32.4 X 10~ 8 cm. It 
is not without interest to observe that a sharp minimum at 1/180,000 
corresponding to a thickness of 32.5 X 10~ 8 cm. occurred in 30 per 
cent of the experiments reported in this chapter. 

We do not wish to lay too much stress on these results. If there 
were no other determinations of the molecular weight than that found 
by this method, our figure would be of limited interest and could only 
be looked upon as a possible estimation which happened to tally with 
the chemical composition. However, when this value is compared 
with the two others obtained by totally different methods, and if the 



STUDY OF THE EGG ALBUMIN MOLECULE 119 

causes of error attached to such determinations are considered, one 
cannot help being struck by the similarity of the figures. The fact 
that they are in such good accord in itself confers a character of prob- 
ability on these values practically as great as would result from the 
useof a theoretically more rigorous and experimentally more accurate 
method. 



Chapter 6. 
Characteristics of Immune Serum. 

Experiments made during the past three years on immune serum 
have given us some interesting and precise information concerning 
their peculiar physico-chemical behaviour. 

It is well known that a normal and an immune serum are totally 
different from a biological standpoint. This is easily ascertained by 
the biological tests, hemolysis, precipitation or agglutination, accord- 
ing to the nature of the antigen used in immunizing the animal. 1 But 
unless the immune serum is placed in contact 'with its specific antigen, 
there is no means of differentiating it from a normal serum. Chem- 
ically, its composition seems the same ; physically, its properties, density, 
viscosity, refractive index, conductivity, etc., are unaltered. 2 Yet, im- 
mune serum is different. 

Certain authorities have observed 3 that in some cases after immuniza- 
tion the percentage of globulins in serum was increased over that of 
the albumin. Lecomte du Noiiy and Baker 3a were unable to demon- 
strate this in experimenting with rabbits. It is, therefore, not gen- 
eral, and, in any case, need not imply any chemical change in the 
constituents of the serum, neither would it explain the phenomena 
which we are about to describe. 

It is not surprising that the usual methods of chemical analysis 
did not enable us to detect the difference in immune serum. It is 
known that a very large number of substances — probably all the pro- 
teins and perhaps other bodies — can act as specific antigens ; that is, are 

1 For certain cases another method has been proposed : the highly interesting 
so-called meiostagmin reaction, worked out by Prof. Ascoli (Munch. Med. Woch. 
1910, LVII, p. 62) and since studied by Waterman and many others, which is 
based on the study of the surface tension of a mixture of immune serum with 
an alcoholic solution of its antigen. 

'However, very recent contributions by L. D. Felton and G. H. Bailey (Bull. 
Johns Hopkins Hosp. 1926, XXXVIII, p. 33) seem to indicate that a modification 
can be detected. 

3 R. Doerr & W. Berger. Z. Hyg. u. Infectionskrankh. 1921, XCIII, p. 147; 
& W. Berger, Z. Ges. Exp. Med. 1922, XXVIII, p. 1. 

* Lecomte du Noiiy & L. E. Baker. J. Exp. Med. 1925. XLII. p. 9. 

120 



CHARACTERISTICS OF IMMUNE SERUM 121 

capable, by reacting with some constituent of the living organism, to 
confer upon it different chemical properties with respect to the same 
antigen. These new properties may protect or sensitise the organ- 
ism, according to the substance injected. 4 But no matter what they 
are, nor of what importance, the fact remains that the nature of 
the chemical substances entering in the constitution of the plasma seems 
unchanged. (See Footnote 2, page 120.) This clearly shows that our 
ordinary chemical methods of analysis are too brutal to maintain as 
entities certain complicated and fragile chemical individuals which exist 
only in the plasma, and which are endowed with specific chemical prop- 
erties deriving from their existence as a unit. Once this individuality 
is destroyed these properties are lost, and the chemist, like the wrecker, 
finds nothing but the stones from which the monument was built. 

It was, therefore, desirable to find a method whereby all the un- 
known chemical individuals could be studied without first destroying 
their individuality. No one can tell as yet how the numerous con- 
stituents of the serum are bound together. The fact that proteins, 
lecithin, fats, fatty acids and cholesterol are found, does not carry with 
it the conclusion that they all exist separately in the serum. We 
know that it cannot be so. As they appear in the serum in solution 
and as some of them are perfectly insoluble when isolated, it is im- 
possible to state at present whether or not a "molecule of serum" does 
not exist as a unit. 

It is quite obvious that the chemical study of such an enormous 
molecule cannot as yet be attempted. It is possible to conceive that 
every active group could react individually, thus changing its prop- 
erties with respect to one single substance, without, however, greatly 
altering the general properties of the whole with respect to other 
simple reagents. But if only a few atoms are shifted, 5 on this mass 
of, say 4000 atoms, or more, or if some new atoms are added to it, 
there must be a slight change in the field of forces surrounding this 
molecule. If all these slight changes could sum up, a relatively im- 
portant modification might be expected. And if, somehow, a large 

4 It is not only against poisonous bodies, but also against wholly or nearly 
inoffensive substances that animals react. 

B The number of possible combinations in such complex substances is beyond 
imagination; as an illustration it may be recalled that twenty people seated 
around a table, that is, in a two dimensional space, can be placed in 20! different 
ways, e.g., 2 billion billion ways. Now one egg albumin molecule contains more 
than 4,000 atoms, distributed in a three dimensional space. The number of pos- 
sible combinations, therefore, although it can be calculated, is impossible to 
conceive. Yet each corresponds theoretically to a definite chemical property. 



122 SURFACE EQUILIBRIA 

number of molecules could be arranged alongside of each other so that 
this addition could take place, it could even, perhaps, be measured. 

This is exactly what was done in producing monomolecular layers 
of serum on water. Something like 130,000 billions of molecules — 
if it be assumed that their cross section is about the same as that of 
the egg albumin molecule — are placed vertically in a sort of geometric 
mosaic. The most minute change in the field of forces binding these 
molecules together will be amplified more than one hundred thousand 
billion times, and the roughest measurement of static surface tension 
may detect it. 

This hypothesis, if it were true, would lead to the somewhat un- 
expected conclusion that the phenomenon of increased time-drop should 
be more marked with highly diluted than with pure serum. 

Consequently, assuming that the watch glasses described in Chapter 1 
are used, it is around the dilution of 1/10,000 that a change in the drop 
of surface tension should be expected. In order to verify this the first 
series of experiments was performed in the following way : 6 

Animals: 31 rabbits, 4 dogs and 18 chickens were used. 15 to 20 cc. 
of blood were removed before the antigen was injected, in order to 
study the normal serum. The same amount was withdrawn 15 days 
after the injection. In certain cases, however, the animal was bled 
every day in order to follow any gradual changes effected. 

Antigen: .Dog serum, white of egg, and red corpuscles of rabbit and 
sheep were used. For the latter, the blood was received in sodium 
citrate solution and centrifuged. The red corpuscles were then washed 
three times in isotonic NaCl solution. Usually 4 intravenous or intra- 
peritoneal injections of 4, 6, 8 and 10 cc. were made. The white of egg 
was injected at 20 per cent in isotonic salt solution. 

Controls: Control animals were bled at the same time as the experi- 
mental animals and received injections of isotonic salt solutions, ho- 
mologous red cells and turpentine (0.3 cc. under the skin). This was 
done in order to make sure that the changes observed were a conse- 
quence of the immunization process and were not due to the injection of 
a non-antigenic substance. The state of immunization of the animals 
was followed, according to the customary methods hemolysis and 
precipitation. 

The results obtained showed clearly that the value of the drop of 
the surface tension in two hours was increased in all the animals 
which had been submitted to an antigenic injection, while the control 
a Lecomte du Noiiy. J. Exp. Med. 1923, XXXVII, p. 659. 



CHARACTERISTICS OF IMMUNE SERUM 



123 



animals did not show any change. Moreover, the above hypothesis 
concerning the magnitude of the phenomenon at different concentra- 
tions was verified. Figures 48 and 49 show that a maximum exists at 
1/10,000 as had been foreseen. 




Concentration 

Fig. 48. — Time-drop curves; i.e., differences between the initial surface tension 
and the surface tension after 2 hours. Normal and immune serum (rabbit). 
The time-drop of the immune serum is nearly double that of the normal 
serum. 

This is probably the first time that the physico-chemical modifica- 
tions of the serum following antigen injection has been demonstrated 
by a direct and purely physical method. 

Dynes 
3 15 



9 10 

I 

1 5 





















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Concentration 



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Iff 



Fig. 49. — Time-drop before and after immunization. Mean curves expressing the 
result of experiments on seven rabbits. 



The existence of a measurable effect being thus ascertained, 
the next step was to study its evolution as a function of the time. 
Table XV expresses the results of a series of experiments with 6 
rabbits and 2 controls. Figures 50 and 51 illustrate two other series, 



124 



SURFACE EQUILIBRIA 



TABLE XV. 

Value of the Time-Drop of the Serum of Six Rabbits During the Process 
of Immunization and of Two Controls. 



Date 


Controls 


Rabbits injected with 
sheep-cells 


Rabbits injected with 
egg white 


Remarks 




No. 1 


No. 2 


No. 3 


No. 4 


No. 5 


No. 6 


No. 7 


No. 8 




1922 


dynes 


dynes 


dynes 


dynes 


dynes 


dynes 


dynes 


dynes 




Sept. 28 


4.5 


6.0 


8.0 


7.7 


6.2 


4.2 


5.2 


4.5 


First injection 


" 29 


3.0 


5.5 


6.0 


7.0 


10.0 


8.0 


10.0 


12.5 




Oct. 2 


4.5 


2.0 


9.0 


7.5 


10.5 


9.5 


9.0 


6.0 




3 


4.5 


5.0 


5.2 


7.5 


6.5 


4.5 


7.0 


5.0 


Second injection 


.4 


2.5 


2.0 


4.5 


4.5 


4.0 


3.5 


4.5 


7.5 




5 


1.5 


3.0 


9.0 


10.0 




8.0 


4.0 


12.0 




6 


1.8 


6.2 


9.0 


12.5 


11.0 


12.7 


13.0 


10.8 


Third injection 


9 


5.0 


11.0 


10.5 


13.0 


7.5 


5.5 


6.5 


10.5 


Fourth " 


" 10 


5.5 


7.0 


11.0 


12.0 


17.5 


11.5 


14.0 


15.0 




11 


8.0 


7.0 


14.5 


13.0 


11.0 


15.5 


17.3 


17.5 




13 


5.5 


7.0 




14.8 


13.5 


13.5 


14.0 


14.0 




" 16 


3.0 


5.5 


Died 


11.0 


13.5 


13.5 


12.5 


10.5 





one with 6, the other with 8 rabbits. In these last cases the control 
curve expresses the mean values obtained with 8 animals. These 
curves are quite analogous to those obtained by plotting as ordinates 




Oct. 












3 


6 


9 


10 11 


13 


16 


5 th 


8 th 


11 th 


12 th 13 th 


15 th 


18 th 



Date 11% 
Day 

Fig. 50. — Curve representing the evolution of the process of immunization. Mean 
values of six experiments on rabbits and three controls (Table I). Only the 
time-drop of serum diluted to 1 : 10,000 was studied. 



the quantity of antibody resulting from similar experiments and titrated 
according to the ordinary methods in vitro. 7 A parallelism seemed 

7 A. Jorgensen & T. Madsen, Festkrift. ved. Indvielsen af Statens, Serum- 
Institut, Copenhagen, 1902, Paper 6, p. 12; and A. Fisher. J. Exp. Med. 1922, 
XXXVI, p. 535. 



CHARACTERISTICS OF IMMUNE SERUM 



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126 



SURFACE EQUILIBRIA 



therefore to exist between the surface tension effect and antibody for- 
mation. It is clear indeed that the experiments made with non-antigenic 
substances did not reveal any disturbance. (Fig. 52.) 

This molecular phenomenon presents, between the 12th and 14th 
day, a maximum in all the cases reported above. After this lapse of 
time, a progressive decrease is observed and by about the 25th day 
the serum seems to have come back to normal. We are too ignorant 
of the structure of the protein molecules even to attempt to explain these 
facts. All that can be done at present is to study them in their relations 
with the so-called antibodies, so as to ascertain whether a physico- 
chemical manifestation due to these hypothetical substances is dealt with, 
or whether the increased time-drop and the formation of antibodies are 
two distinct phenomena consecutive to the antigen injection. First of 
all it was necessary to determine whether the same results could be 
expected from bacterial immunization and from vaccine virus. This 
was proved to be the case for Bacillus coli and vaccine virus, which 
yielded results identical to those described above. 8 The results of a 
series of experiments made with Dr. Noguchi's vaccine virus are given 
in Tables XVI and XVII. The immunization of the rabbits was checked 
by a later revaccination. An increase in the value of the time-drop 
varying between 18 and 130 per cent may be observed on the 13th day. 

TABLE XVI. 

Time-Drop of 1/10,000 Solutions of Rabbit Sera Before and After 

Vaccination. 



No. 



flnitial value 

1 \ After 2 hrs. 

[ Time-drop . 

flnitial value 

2 \ After 2 hrs. 
I Time-drop . 

flnitial value 
7 { After 2 hrs. 
I Time-drop 



flnitial value 

8 i After 2 hrs. 

[Time-drop . 



Normal 



dynes 

64.0 

55.0 

9.0 

63.0 

54.5 
8.5 

66.0 
56.0 
10.0 

69.5 
58.0 
11.5 



13 days after 
vaccination 



dynes 

75.0 

57.5 
17.5 

76.0 
56.5 
19.5 

73.5 
S7S 
16.5 

76.0 
58.5 
17.5 



Increase in time-drop 



per cent 



94 



130 



65 



52j 



Immune 



Lecomte du Nouy. J. Exp. Med. 1924, XI, p. 129. 



CHARACTERISTICS OF IMMUNE SERUM 



127 



TABLE XVII. 

Time-Drop of 1/10,000 Solutions of Rabbit Sera Before and After 

Vaccination. 



No. 9. 



10, 



" 3. 



" 4. 



" 6. 



Initial value 
After 2 hrs. 
Time-drop . 

Initial value 
After 2 hrs. 
Time-drop . 

Initial value 
After 2 hrs. 
Time-drop . 

Initial value 
After 2 hrs. 
Time-drop . 

Initial value 
After 2 hrs. 
Time-drop . 

Initial value 
After 2 hrs. 
Time-drop . 



Normal 


13 Days 

After 

Vaccina- 




tion 


Dynes 


Dynes 


70.0 
58.0 
12.0 


76.0 
61.0 
15.0 


68.0 
57.0 
11.0 


75.5 
62.5 
13.0 


76.0 

67.2 

8.8 


77.0 
65.5 
11.5 


73.5 

65.0 

8.5 


76.5 
59.8 
16.7 


75.5 
65.5 

10.0 


77.0 
64.0 
13.0 


75.5 

66.5 

9.0 


77.0 
66.0 
11.0 



Reaction 



Good up to 
a dilution 
of 1/10. 



1/10 



1/10 



1/10 



1/100 



1/10 



Increase in Time- 
Drop 



Per Cent 



25 



18 



31 



97 



30 



22 



Immune. 



It will be noticed that this phenomenon is essentially non-specific; 
that is to say that totally different antigens affect the drop in surface 
tension in the same way. 

During the course of the preceding experiments, which lasted about 
sixteen months, great difficulty was encountered in securing absolutely 
normal animals. The value of the time drop of fresh animals sup- 
posedly normal varies between 6 and 18 dynes without any appar- 
ent reason. Now an animal with a time-drop of 18 dynes will show 
no increase, or very little, in this value if it receives an antigenic 
injection. The conclusion was, for rabbits, for instance, that an ani- 
mal, even though considered normal and of healthy appearance, but 
which shows a time-drop of more than 10 dynes, has antibodies in 
its circulation and is unsuitable for experimental purposes. In a lot 
of 25 fresh rabbits it frequently happened that 15 had to be dis- 
carded. The eliminated ones were kept under observation and most. 



128 SURFACE EQUILIBRIA 

of them showed positive symptoms of snuffles within a few days. 
Some of them died and yet, at the time of their delivery in the 
laboratory, there was nothing but the abnormal time-drop value to 
indicate the possibility of such an epidemic. Those which did not subse- 
quently develop snuffles, although showing a time-drop of over 10 dynes, 
were probably recovering from the same disease and were, therefore, 
also unfit for experimental purposes. 

From that time on, therefore, no animals showing a time-drop higher 
than 10 dynes were used, and the phenomenon following immunization 
was observed regularly. 

This observation, which makes it possible to effect a rigorous selec- 
tion among animals and to obtain constant results for such experiments 
on immunity, indicates that, so far as man is concerned, the study of 
the time-drop will probably fail to yield useful information, unless in 
the case of very young children. 

Experiments showed, indeed, that the normal time-drop for the adult 
man varied between 15 and 22 dynes. The serum of 67 children, of 
from 6 months to 8 years old, treated at the Babies' Hospital in New 
York City, 9 gave results which can be summarized as follows : 

Time-drop in dynes : 16 to 20 14 to 16 12 to 14 10 to 12 7 to 10 

Number of children: 33 16 11 4 2 

All except three of these children had received an injection of diph- 
theria anti-toxin. One of those which showed a drop between 7 and 
10 dynes (8.7), had not yet received this injection and another (6 
months old) had received it only three days before the bleeding. Neither 
had an infectious disease. It is difficult to draw any conclusion, except 
that it is probably impossible to find in a human being a serum entirely 
devoid of some kind of immunity, either natural or acquired. 

Many problems arose as a consequence of the preceding experiments. 
Our knowledge of the phenomenon depended on their solution. 

1. Did the increase in the time-drop of surface tension after the 
antigen injection really correspond to a decrease in the absolute static 
value of the surface tension? 

2. Except in the case where vaccine virus was used and simply 

smeared on the skin, the animals had received from 3 to 4 injections of 

antigen. What would happen if only one injection were made? Would 

the maximum drop occur after the same number of days or after a 

shorter period of time, and would the drop be of the same magnitude? 

9 1 wish to express to Dr. M. Wollstein of the Babies' Hospital, my deepest 
gratitude for the help and facilities extended to me in this work. 



CHARACTERISTICS OF IMMUNE SERUM 129 

3. Is the magnitude of the drop a function, within certain limits, of 
the amount of antigen injected? 

4. Is the thickness of the adsorbed monolayer affected in a measur- 
able way by immunization? In other words, is this change in the 
individual field of forces of every molecule accompanied by a change 
in the length of the molecule? 

5. Would a new antigen injection given immediately after the maxi- 
mum (around the 13th day) result in an increase of the effect or would 
it delay its decrease? 

6. Could the phenomenon be repeated by injecting a new amount 
of antigen on the 30th day when the serum seems to have returned 
to normal? In other words, has the serum undergone a more or less 
permanent modification or a temporary one? 

7. Could it be that the phenomenon is merely due to the presence of 
antigen in the circulation? 

8. Is there a change in the relative proportion of globulins and 
albumin on the 13th day? 

9. In what way is this phenomenon related to the so-called antibodies ? 
These problems will be taken up successively. Several of them can 

be elucidated by one type of experiment, which will, therefore, be 
described in detail. 10 

Twelve rabbits were chosen, six of which were used as controls. 
All of these animals were isolated and studied for a period of two 
months before the injection, in order to make certain that they had nor- 
mal time-drops of less than 10 dynes. They were bled three times during 
this period and were found to be normal. The experimental animals 
were then injected intravenously with an antigen made from crushed 
horse kidney, 11 provided by Dr. Landsteiner. This antigen was chosen 
because of its harmlessness and its constant results. In previous work 
some trouble had been experienced with other antigens. One of the 
animals died just before the experiment was started, so only five were 
left in addition to the controls. Rabbit 1 received 4 cc. of the antigen ; 
rabbits 2 and 3 received 5 cc. ; rabbits 5 and 6 received 10 cc. All 
were, of course, kept and fed in the same way as the controls. Meas- 
urements were made every other day. Crosses indicate the time of 
the bleedings in Table XVIII. 

10 Lecomte du Noiiy. J. Exp. Med. 1925, XLI, p. 779. 

"The horse kidney is crushed and diluted to 1/10 with physiological salt solu- 
tion (NaCl 0.9%). 0.5% of phenol is added as preservative. The mixture is 
allowed to settle and the supernatant fluid is used. 



130 



SURFACE EQUILIBRIA 



TABLE XVIII. 



Day After Antigen Injection 


5 


6 


7 


8 


9 


12 


13 


15 


16 

A 


19 


20 

X 


n 


23 
X 


26 


27 
X 


28 




[No. 1 


X 




X 




X 


X 


X 






" 2 


X 




X 




X 


X 


X 




X 




X 




X 




X 




Controls 


" 4 


X 


X 


X 


X 


X 


X 
X 


X 
X 


X 


X 


X 


X 


X 


X 


X 


X 


X 




" 5 




X 




X 




X 


X 


X 




X 




X 




X 




X 




" 6 




X 




X 




X 


X 


X 




X 




X 




X 




X 




f No. 7 


X 




X 




X 


X 


X 




X 




X 




X 




X 






" 8 


X 




X 




X 


• 


X 




X 




X 




X 




X 




Experimental 


" 9 




X 




X 




X 


X 


X 




X 




X 




X 




X 




" 10 




X 




X 




X 


X 


X 




X 




X 




X 




X 




" 11 




X 




X 




X 


X 


X 




X 




X 




X 




X 



It will be seen that the controls and the experimental animals were 
bled alternately, except on the 12th and 13th days when the time-drop 
phenomenon was expected to reach its maximum. The reasons for 
not making the measurements every day were, first, that the animals 
might be disturbed by too frequent bleedings, and secondly because 
of technical difficulties. It must be borne in mind that 17 different 
dilutions of the serum were made in each case. This in itself re- 
quired considerable glassware which had to be cleaned with the utmost 
care. As two measurements of the surface tension were required at 
2 hours' interval, this meant 34 measurements for each serum. When 
all sera were dealt with, as on the 12th and 13th days, 374 measure- 
ments of surface tension had to be made in one day. This amount 
of labour can be carried out during two days, but it becomes extremely 
taxing on all concerned when done oftener. Fortunately this appeared 
to be unnecessary. As it was, the first set of experiments reported 
here required a total sum of 4420 measurements of surface tension. 
This was rendered possible by the simultaneous use of three tensiome- 
ters on the tables described in Chapter 2. 

The seventeen different dilutions of every serum were made because 
it was important to know whether the maximum drop, or absolute 
minimum of static surface tension, always occurred at the same dilu- 
tion, or whether it was slightly shifted, perhaps as a consequence of 
the injection of antigen. The following dilutions were studied : 1/10 
1/100; 1/1,000; 1/7,500; 1/8,000; 1/8,500; 1/9,000; 1/9,500 
1/10,000; 1/10,500; 1/11,000; 1/11,500; 1/12,0D0; 1/12,500; 1/13,000 
1/100,000; 1/1,000,000. The dilutions 1/10,500 and 1/11,000 corre- 
spond to a difference in thickness of the adsorbed layer of, roughly, 



CHARACTERISTICS OF IMMUNE SERUM 



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132 



SURFACE EQUILIBRIA 



TABLE 

Dilution at Which the Minimum Value of Surface Tension 



Rabbit No. 


Mean 
value of 
measure- 
ments 
made be- 
fore in- 
jection of 
antigen 


Day after antigen 




5 


6 


7 


8 


9 


12 


13 


15 


1 
2 
3 
4 
5 

Controls 
6 
7 
8 


i : 10.000 
1:10,000 
1:10,500 
1:10,500 
1:10,500 

1:10,500 
1:10,500 
1:10,500 


1:10,500 

1:10,500 
1:11,000 


1:10,000 
1:11,000 

1:10,000 
1:10.000 
1:10,500 


1:10,000 

1:11,000 
1:11,000 


1:10,000 
1:11,000 

1:10,500 
1:10,000 
1:11,000 


1:10,000 

1:11,000 
1:10,500 


1:10,000 
1:10,000 
1:11,000 
1:10,500 
1:11,500 

1:10.500 
1:10,500 
1:11,000 


lrl0,500 
1:10,000 
1:10,500 
1:10,500 
1:11,000 

1:10,00C 
1:10,500 
1:10,500 


1:10,500 
1:11,000 

1:10,500 
1:10,500 
1:11,000 


Mean value of experi- 
ments. 

Mean value of controls. 
" " all ex- 
perimentals. 

Mean value of all con- 
trols. 


1:10,666 

1:10,517 
1:10,400 


1:10,500 
1:10,166 


1:10,666 


1:10,500 
1:10,500 


1:10,500 


1:10,600 
1:10,333 


1:10,500 
1:10,333 


1:10,750 
1:10,666 



2 X 10~ 8 cm. As the thickness of the monolayer of whole rabbit serum 
is nearly 41 X 10~ s cm., this means that a change in the thickness of 
about 5 per cent could be detected in this vicinity. On taking into 
account the working conditions and the variations likely to arise from 
changes in the concentration of the proteins over a period of three 
months in the life of the animal, this was considered as the maximum of 
accuracy that could reasonably be expected. 

Table XIX gives the concentrations at which the minimum sur- 
face tension was observed for the five experimental and two con- 
trol animals. It is obvious that no constant shift occurs after im- 
munization. Such differences as were noted may be laid to experi- 
mental errors. It follows that no variation greater than 5 per cent 
occurs in the mean length of the protein molecules after immuniza- 
tion. This answers question 4. 

The answers to questions 1, 2, 3, 5, 6 are to be found in Figures 53 
to 57. Figure 58, in which the time-drop is plotted, summarises the 
results. 

It is clear that in all cases an absolute minimum of the static value 
of surface tension is observed (question 1) and that the minimum 
occurred practically after the same number of days (between the 12th 
and 16th) whether the animals received 1 or 4 injections of antigen 
(question 2). It is also probable that, to a certain extent, the absolute 



CHARACTERISTICS OF IMMUNE SERUM 



133 



XIX. 

Occurred in Five Experimental Animals and Three Controls. 

injection 



16 


19 


20 


21 


23 


26 


27 


28 


29 


30 


1:10,000 

1:10,500 
1:10,500 


1:10,500 
1:10,500 

1:10,500 
1:10,500 
1:10,500 


1:10,500 

1:10,500 
1:10,500 


1:10,000 
1:11,000 

1:11,000 
1:10,500 
1:10,000 


1:10,500 

1:10,500 
1:10,500 


1:10,500 
1:10,500 

1:10,500 
1:10,000 
1:10,000 


1:10,500 

1:10,500 
1:10,500 


1:10,500 
1:11,000 

1: 10,500 
1:10,500 
1:10,500 


1:10,500 

1:10,500 
1:10,000 


1:11,000 
1:10,500 

1:10,000 
1:10,500 
1:10,500 


1:10,333 


1:10,500 
1:10,500 


1:10,500 


1:10,500 
1:10,166 


1:10,500 


1:10,500 
1:10,166 


1:10,500 
1:10,500 


1:10,750 
1:10,500 


1:10,333 


1:10,750 
1:10,333 



value of the minimum is a function of the quantity of antigen in- 
jected. Rabbit 5 reaches on the 12th day the extremely low value 
of 50 dynes, which is less by 18 dynes than its normal static value. 
Rabbit 4 reaches 51 dynes. Both had received 10 cc. of antigen (ques- 
tion 3). On the 15th day they each received another injection of 
antigen equal to the first, i.e. 10 cc. No change in the curve resulted. 
It appears from these findings that an injection of antigen immedi- 
ately after the maximum does not result in an increased effect (ques- 
tion 5) and that the increased time-drop is not due to the presence of 
antigen in the circulation (question 7). 

Rabbits 1, 2 and 3 received a second injection of the same amount 
of antigen on the 30th day. They were bled 13, 14 and 15 days later 
and their serum did not show any decrease in the static value of their 
surface tension. This experiment was repeated on other animals with 
the same negative result. 12 The serum had, consequently, undergone 
some kind of change of a more permanent nature (question 6). 

On the other hand, the amount of antibodies, as indicated by the 
hemolytic test in vitro, was increased. It therefore seems as if the 
phenomenon revealed by the existence of the minimum value of the 

13 It sometimes happens that the static value at the end of the first period of 
30 days is higher than at the beginning. It usually retains this value for some 
months. 



134 



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CHARACTERISTICS OF IMMUNE SERUM 



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CHARACTERISTICS OF IMMUNE SERUM 



139 



static tension is not directly correlated to the presence of antibodies, but 
that the two phenomena are simply co-existent at the beginning of 
immunization. These two manifestations of the state of immunity 
differ not only in their duration, but also in the fact that a subsequent 
injection of antigen, while it determines a recrudescence in the antibody 
content, does not cause a reappearance of the minimum. 13 It thus ap- 
pears as if the serum had undergone a deeper change which parallels 

y^Q S ContPOl experiments 

65 

60 

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D&ysO 123456789 10 11 1213 1415 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 

Fig. 59. — Static values, after 2 hours, of normal rabbit sera (controls), in the 
same conditions as the experiments reported on Figs. 53 to 57. 



the immunity itself. At the present "time it is impossible to answer 

question 9 more definitely. 

Figures 59 and 60 express the result of measurements made with 

the serum of the controls and the values of the initial surface tension 

of solutions during a series of experiments. It will be seen that this 

value is practically constant throughout the series. The above discussed 

phenomenon manifests itself only by its action on the static value of 

the solutions after two hours standing. 

"We have reasons to believe (unpublished experiments in course of realisa- 
tion) that when a different antigen is used for the second injection, a reappear- 
ance of the minimum occurs. 



140 



SURFACE EQUILIBRIA 



So far as the change in the percentage of globulins and albumin is 

concerned, it can be stated that the phenomenon in question is entirely 

independent of it. A series of analyses were made by Dr. Baker 14 on 

the sera of animals immunized with bacillus coli, sheep cells, egg 

albumin and organ extracts. The results of these analyses showed 

.1 .1 • albumin ..-,., , . f 

that the ratio . , .. — varies little, and certainly not more in the lm- 
globulm J 

munized animals than in the controls. It will be seen in Table XX that 



Dynes 
18 
T6 



a 

2 72 



Mean value of initial values before and after immunization. Dilution 1/10,500 





















































r-:':r 


;injec 




rabfc 


its) 












After inject: 


on E 


pat 


(its) 




















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31 24 24 13 

Oct Nov. Dec. Jan. 

1924 1925 



11 13 15 17 19 21 23 25 27 29 31 



2 
Feb. 



Fig. 60. — Mean value of initial surface tension, before and after immunization. 
The figure shows that the increased time-drop is due to an actual decrease in 
the static value of the surface tension, and not to a change in the initial value. 



in one series of experiments, the controls showed a greater decrease 
of the ratio -?? than the experimental animals. 

An attempt was made to answer question 7 more definitely still 
(action of the antigen on the serum). The normal serum of 7 rabbits 
was mixed with an amount of different antigens corresponding to the 
quantity used for immunization. 15 The mixture was then kept in the 
incubator at 37° for 13 days. The time-drop was measured before the 
addition of antigen and at the end of the 13th day. No increase was 
observed in the value of the time-drop which remained about 10 dynes. 
It may, therefore, be concluded that, as is the case for immunization, 
the presence of living cells is required to produce the phenomenon of 
the decrease of surface tension. 

In certain cases the disturbance undergone by the molecules around 
the 13th day, when the phenomenon reaches its maximum, manifests 

"Lecomte du Noiiy & L. E. Baker. J. Exp. Med. 1925, XLII, p. 9. 

"Lecomte du Noiiy & L. E. Baker. Loc. cit. For more ^ information con- 
cerning these experiments and the preceding ones, the reader is referred to the 
protocols given in the original paper. 



CHARACTERISTICS OF IMMUNE SERUM 



141 



TABLE XX. 

Proportion of Albumin and Total Globulins in Rabbit Serum (in 

Percentage). 



Nos. 


Before Immunization 


After Immunization 
(13th day) 




1 


2 


3 


4 


5 


1 


2 


3 


5 




69 

31 

2.22 


71 
29 

2.45 


78 

22 

3.50 


76 
24 

3.16 


71 
29 

2.45 


71 
29 

2.45 


69 
31 

2.22 


74 
26 

2.85 


73 




27 


Ratio— 


2.70 






Mean value of the 
ratios 


275 


2.56 









Control Animals. 








Nos 




Before Immunization 


After Thirteen Days 




1 


2 


1 


2 




75 
25 

3 


78 
22 

3.50 


70 
30 

2.35 


77 




23 


Ratio — 


3.35 






Mean value 


of 


the ratios. .. . 


3.25 


2.75 



TABLE XXI. 
Refractive Indices of Immune and Normal Sera. 







Controls 


Rabbits injected with 


Rabbits injected with 


Dat 


e 


sheep cells 


egg white 




No. 9 


No. 10 


No. 11 


No. 12 


No. 13 


No. 14 


No. 15 


No. 16 


1922 


















Sept. 


28 


1.3438 


1.3429 


1.3442 


1.3422 


1.3440 


1.3433 


1.3438 


1.3429 


" 


29 


1.3398 


1.3392 


1.3399 


1.3385 


1.3402 


1.3390 


1.340/ 


1.3325 


Oct. 


2 


1.3398 


1.3386 


1.3409 


1.3390 


1.3408 


1.3397 


1.3410 


1.3381 






3 


1.3440 


1.3387 


1.3404 


1.3398 


1.3405 


1.3405 


1.3420 


1.3390 






4 


1.3388 


1.3384 


1.3395 


1.3388 


1.3400 


1.3398 


1.3399 


1.3392 






5 


1.3398 


1.3393 


1.3408 


1.3350 




1.3395 


1.3401 


1.3385 






6 


1.3422 


1.3415 


1.3415 


1.3410 


1.3420 


1.3440 


1.3415 


1.3420 






9 


1.3415 


1.3413 


1.3401 


1.3420 


1.3402 


1.3405 


1.3411 


1.3405 






10 


1.3400 


1.3388 


1.3391 


1.3402 


1.3403 


1.3403 


1.3398 


1.3391 






11 


1.3391 


1.3385 


1.3391 


1.3383 


1.3396 


1.3396 


1.3390 


1.3386 






13 


1.3399 


1.3385 


Died 


1.3385 


1.3383 


1.3390 


1.3391 


1.3391 






16 


1.3389 


1.3385 




1.3370 


1.3390 


1.3384 


1.3392 


1.3390 


Average 


1.3400 


1 3400 








1 


















Dilution 

of serum... 1:10,000 



1:10,500 1:11,000 1:11,500 

Normal serum in 0.9 per cent NaCl solution (control). 




Dilution 

of serum... 1:10,000 



1:10,500 1:11,000 

Immune serum No. 7 in 0.9 per cent NaCl solution. 



1:11,500 




Dilution 
of serum 



1:10,000 1:10,500 1:11,000 

Immune serum No. 8 in 0.9 per cent NaCl solution. 



1:11,500 



Plate IX. — Photographs, slightly reduced, of watch glasses after evaporation of 
the solution. The top row a is a normal serum (control). The two lower 

. rows, b and c, are immune sera. In these two series the NaCl crystals at the 
dilution 1:10,500 are quite different from those of the normal serum, and 
also from those of other concentrations (1:10,000 and 1:11,000). 



142 



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Fig. 3. 
Plate X, Fig. 2. — A photomicrograph of the area delimited in black on the first 

row, a of Fig. 1 (concentration 1:10,500), normal serum. X 10. 
Fig. 3. — A photomicrograph of the area delimited in black on the last row, c of 

Fig. 1 (concentration 1:10,500), immune serum. X 10. 
Both photomicrographs were taken with polarized light, through a blue filter. 

143 



144 SURFACE EQUILIBRIA 

itself in strongly immunized animals in a very striking- manner 
by its action on the crystallisation of the NaCl in the solution. The 
reader is referred to Plates IX and X, where the differences observed 
in the structure of NaCl crystals before and after immunization are 
exhibited. The existence of such a modification in the molecules could 
be expected to manifest itself by other physical phenomena, such, for 
instance, as a variation in the refractive index. Table XXI shows that 
such is not the case. 



Chapter 7. 

Influence of Colloids on the Crystallisation of 
Sodium Chloride. 

The following phenomenon is generally observed when a solution 
containing colloids and crystalloids in certain proportions is allowed 
to evaporate at room temperature. Instead of concentrating in the bulk 
of the liquid, as in the case of pure saline solution, and forming at the 
bottom of the watch glass well denned cubic crystals as those of Plate 
XI (bottom row), a certain number of NaCl molecules are adsorbed 
on the colloidal molecules and follow them to the surface. The evapora- 
tion of the solution no longer results in a concentration of the salt and 
very small crystals spread all over the watch glass as the liquid creeps 
down and assume different aspects according to the concentration. 

Considering the considerable excess of the number of NaCl mole- 
cules over the number of protein molecules in our experiments, it is 
probable that the salt cannot all be adsorbed and that capillarity plays 
a part where the angle of contact exists between the solution and the 
glass. The last drop of solution remaining in the glass is poorer in 
salts than the initial solution and therefore abandons sparsely distributed 
crystals (Plate XI). 

It seems, therefore, as though, in the case of complex solutions (col- 
loids and crystalloids), Gibb's law were no longer entirely valid, since 
it states that substances which increase the surface tension (crystal- 
loids and crystalloids), Gibb's law is no longer entirely valid, since 

1 The phenomena which take place at the contact of the glass are far from 
being clear. It has been shown (p. 30) that by flaming the watch glasses a 
perfect adherence was obtained. Generally, however, the crystals of NaCl 
abandoned by the solution after evaporation differ according to whether the 
glass has been flamed or not. A Bunsen or an alcohol flame acts approximately 
in the same way; but old glass behaves differently from new glass. Plate XIV 
will make the preceding clear. It is necessary in order to study the action of solu- 
ble substances on the crystallisation of NaCl, not to flame the glasses at all but to 
wash them until they wet perfectly and use them immediately after. The part 
played by the nature of the walls of the vessels in certain reactions depending 
on adsorption is little known but of great interest. A striking example of this 
phenomenon was given by Kohlschiitter in 1908 (Zeit. f. Elektrochemie XIV, p. 
49). While preparing colloidal silver according to his own method, viz., the 

145 



146 



1:100 



SURFACE EQUILIBRIA 

1:1,000 



1:100,000 



1 :500,000 



1 :200,000 



1:600,000 



NaCl 0.9 per cent NaCl 



1:10,000 





N^ 





1:400,000 




1 :800,000 



~~ x 


/ 


'^X 




&£%*$ 


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mU~***^ #!■ 


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NaCl 



1 %» 


/ 


St 



Plate XI. — Crystals of serum solutions in NaCl solution at 0.9 per cent (rabbit) 



INFLUENCE OF COLLOIDS 147 

inspection of Plates XI to XIII reveals the fact that a trace of colloids 
is sufficient to displace the crystalloids from the bulk of the solution 
toward the surfaces. Another interesting fact is the appearance at 
certain concentrations of more or less regular concentric rings. This 
occurs, for instance, at a dilution of about 1/100 for serum and 1/1,000 
for saponin. Sodium oleate, glycocholate and taurocholate act in the 
same way. 2 

The concentration of salts at interfaces, brought about by the 
above phenomenon, may throw some light on certain hitherto un- 
explained facts. For example, a phenomenon observed and studied 
by Macallum, 3 i.e. the accumulation of potassium at interfaces in vege- 
table and animal cells, can be explained to a certain extent. The ap- 
pearance of protein membranes at interfaces also becomes clearer. The 
concentration of proteins alone could not well account for precipitation 
or coagulation, but the presence of salts facilitates an explanation. The 
presence of the dark central spot in Plates XI to XIII, which in reality 
is a more transparent area in the watch glass due to the lower concen- 
tration of the solution, can be easily explained. The organic molecules 
in solution adsorb the salt molecules and ions and travel to the inter- 
faces in order that the free energy of the system be reduced. Those 
which are adsorbed in the free surface decrease the surface tension, 
but at the same time considerably increase its superficial viscosity (see 
Chapter 9). In other words, a semi-solid and sometimes, in the case 
of monolayers, a solid film is formed at the surface. It is to be ob- 
served that the aspect of the crystals is different when the evaporation 
of a serum solution at 1/10,000, in saline, is retarded by a slow stream 

reduction of silver oxide in water by hydrogen, he found that the reduction 
takes place on the walls of the vessel and not in the liquid itself. The color of 
the sol depends upon the nature of the walls without there being any question 
of the solubility of the glass, so far as can be ascertained. Walls composed of 
soft glass or quartz give yellowish brown hydrosols, while Jena glass gives red, 
reddish brown or blue. With platinum walls no sol formation takes place, but 
instead, crystalline silver separates out. It is obvious, as Zsigmondy points out, 
that the surface of the glass has a vital role to play in the form and size of the 
particles (Chemistry of Colloids, Wiley, 1917, p. 117). Quite lately Dr. Horo- 
witz of the Physical laboratory of the University of Toronto has found some 
very interesting facts that agree with Kohlschutter's observations and our own. 
(Personal communication.) 

2 This ring formation reminds one of the phenomenon known as Liesegang's 
rings, from which, however, it differs fundamentally inasmuch as it occurs 
merely on evaporation, while the Liesegang phenomenon is obtained by adding a 
certain amount of silver nitrate solution to a solution of gelatine and potassium 
dichromate. (R. E. Liesegang, Zeit. Chem. u. Indust. Kolloide, 1907-8, II, p. 70.) 
3 A. B. Macallum. Oberflachenspannung u. Lebenserscheinungen, Ergebn. der 
Physiol., XI, & University of Toronto Studies, 1912, series No. 8. 



148 



SURFACE EQUILIBRIA 
1:10 1:100 




1:1,000 



1:10,000 




1:100,000 



1:1,000,000 




Plate XII. — Crystals of serum solutions in NaCl solution at 0.9 per cent. 

Rabbit serum. 



INFLUENCE OF COLLOIDS 



149 



1:100 



1:1,000 




1:10,000 



1:100,000 




1:1,000,000 


1:10,000,000 


I -mv^' -^B 


mm %&bto mm'-'*-~ i 
mm '^Of 1 ! 




^K '• t^CR, ■ v '^B.?. v" 



Plate XIII. — Crystals of saponin solutions in NaCl solution at 0.9 per cent. 



150 



SURFACE EQUILIBRIA 



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INFLUENCE OF COLLOIDS 



151 



of moist compressed air, so as to take 6 or 7 days. Another modification 
takes place when a flow of nitrogen or of carbon dioxide is used instead 
of air. (Plate XV.) 

The formation of concentric crystalline rings which characterises cer- 
tain concentrations (around 1/100 for serum) can be explained if it 
be assumed that around this concentration the tenacity of the film, due 
to its thickness, is such that the tearing takes place at the periphery 
and not in the center. The whole film, therefore, floats freely until 
the evaporation has lowered the level and it is brought in contact with 




Plate XV. — Serum solutions at 1/10,000 in 0.9 per cent NaCl solution evaporated 

in 6 days under 

No. 1— N 
2 — Co 2 
3— Air 



a lower section of the glass having a smaller* diameter. Adherence 
again takes place circularly and the same process repeats itself until 
evaporation is completed. Each tearing determines the appearance of 
a ring. The central spot is generally richer in NaCl crystals than at 
lower concentrations. The irregularities observed in the rings are due 
to the fact that the film does not tear itself simultaneously on all its 
periphery, and may remain stuck at one or more points to the glass. 
(Plate XII.) 4 



4 The preceding is the writer's interpretation of the phenomena. The reader 
may be interested in another interpretation of the same facts which Dr. K. 
Horowitz personally communicated to the writer. Dr. Horowitz believes that 
the peculiar aspects of the crystals can be explained by assuming that the colloid 
molecules are absorbed on the NaCl crystals, acting as nuclei. Thus each nucleus 
is coated with colloids and deposited near the place where it originated. This 



Concentration 



1 752.000 



1/753,000 



1/754,000 



1/755,000 




Concentration 



1/748,000 



1/749,00 



1/750,000 



1/751,000 



P LATE : Vl-Sodi- o f te U, co^centrati t 1/74 8^00 ^W*£"£ 

dXn fadded^toW NaQ Zion^'IKnoVayer occurred at 1/751,000 as 

aspect of the Sodium Chloride crystals is quite different from the otners. 

152 



INFLUENCE OF COLLOIDS 



153 



8 



8 

™ 



u 




154 SURFACE EQUILIBRIA 

Aspect of Crystals at the Critical Concentrations. 

1. Sodium oleate. Monolayers. 

Plates XVI and XVII require, so to speak, no explanation. It will 
be very clearly seen that the orientation of molecules in a monolayer 
has determined a peculiar structure in the crystals of NaCl. In these 
experiments, the oleate was dissolved in a 1 per cent solution of NaCl. 
The phenomenon is more rarely observed at 1/1,220,000 and at 
1/1,390,000, than at 1/750,000. A slight displacement of the minimum 
of surface tension is sometimes observed when sodium oleate is dis- 
solved in such a saline solution— 1/748,000 and 1/1,218,000, in the 
present case, instead of 1/750,000 and 1/1,220,000. But this is of the 
order of magnitude of experimental errors. 

2. Immune Serum. 

Plates IX and X, Chapter 6, illustrate the appearance after evapora- 
tion of the crystals of normal serum (top row) and of immune serum 
13 days after the antigen injection. A striking difference is visible at 
the concentration of 1/10,500, corresponding to the monolayer in the 
case of this particular serum. The deep-seated modification following 
immunization is even clearer in the microphotographs (Plate X). This 
structure has never been observed in normal serum but only in the serum 
of strongly immunized animals between the 12th and 15th days after the 
antigen injection. 

process is repeated till the greater part of the colloids is absorbed and deposited. 
Evaporation goes on, leaving finally a central drop practically free from colloids. 
Thus, small crystals are free to grow at the bottom. The writer cannot help 
feeling that it is difficult to admit that the bottom drop is free from colloids. 
Among other facts which seem to support an opposite view, the existence of differ- 
ences between the rates of evaporation of different solutions as well as the aspect 
of crystals at the critical concentrations may be mentioned. (See chapter 3.) 



Chapter 8. 

Surface Equilibrium of Complex Colloidal 
Solutions. 

Antagonistic Effect. 

It has been demonstrated in the preceding chapters that the surface 
tension of colloidal solutions decreases as a function of the time as 
soon as the liquid is no longer stirred. Left to itself the system imme- 
diately tends towards a state of equilibrium which is predictable by the 
laws of thermodynamics and which corresponds to the minimum of free 
energy compatible with its total energy. 

This is achieved by the concentration of the molecules of the solute 
in the surface layer of the solvent, which results in a lowering of the 
surface tension. This phenomenon is known as "positive" adsorption. 
The tension then decreases progressively and finally reaches a minimum 
value which is the static value of the surface tension. This, with a few 
exceptions, takes place in all cases in which only one colloid exists in the 
solution. The addition of a trace of powdered sodium oleate, for 
instance, lowers the surface tension of water permanently. But if the 
same amount of sodium oleate, 1/10,000 in weight, be added to 2 cc. 
of serum in a watch glass, an entirely different phenomenon is observed. 
The surface tension of the serum drops to a very low value in a few 
seconds (from 58 dynes to 39 dynes, for instance), but starts increas- 
ing according to a logarithmic law immediately afterwards, and reaches 
its former value (58 dynes) in 7 or 8 minutes as though nothing had 
happened. (Table XXII and Figure 61.) 

It will be seen that in order to study the phenomenon it is necessary 
to take measurements at 15 or 30 second intervals at the beginning. 1 

In other words, the action of sodium oleate on water is neutralised 
by the presence of serum molecules. The same phenomenon takes 
place when other strongly surface active substances, such as sodium 
taurocholate and glycocholate, are used. It explains why the liberation 

^ecomte du Noiiy, J. Exp. Med. 1922, XXXVI, p. 115; & C. R. Soc. Biol. 
1923, LXXXIX, p. 1148. 

155 



156 



SURFACE EQUILIBRIA 





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EQUILIBRIUM OF COMPLEX COLLOIDAL SOLUTIONS 157 



TABLE XXII. 

Rise of Surface Tension of Serum as a Function of Time after a Drop Due 
to the Addition of Sodium Oleate. 

Undiluted Dog Serum. Temperature 2 2° C. 

About 1/10,000 by weight of powdered sodium oleate was used. 



Time 


Surface tension 


Before addition of sodium oleate . . ■. . . . 


dynes 
57 5 


After " " " " 


39.0 


" 15 sec 


44.0 


" 30 " 


48.0 


1 min .♦ 


51.0 


" 1.5 " 


52.5 


2 " 


53.5 


3 " 


55.0 


4 " 


56.8 


5 " 


57.3 


6 " ... 


57.6 


« g u 


58.0 


" 20 " 


57.6 



TABLE XXIII 

Rise of Surface Tension of Serum Solutions after a Drop Due to the 
Addition of Sodium Oleate. 



Rabbit Serum, Diluted in Isotonic NaCl Solution. 
Sodium oleate, 10" 4 , was used. 



Temperature 22 C. 





Surface Tension 


Time 


Concentration of Serum 




1/10 


1/20 


1/100 


1/1,000 


1/10,000 


Before addition of sodium oleate 

After " " " " 

" 1 min 


dynes 

62.5 
38.5 

46.0 

48.5 

51.0 

55.9 

55.0 
56.5 


dynes 

62.0 
37.0 
39.0 
41.5 
42.8 
44.4 
45.0 
46.0 
47.0 

51.0 

56.0 


dynes 

64.0 
38.4 
38.5 
38.5 

40.0 
41.0 
41.7 

42.6 
43.3 
44.0 


dynes 

69.5 
34.5 
34.5 
34.5 
34.5 
34.6 
34.7 
34.8 

35.0 
35.2 
35.7 
36.5 


dynes 

72.0 
35.6 
35.6 
35 6 


2 " 


3 " 


35 6 


" 4 « 


35.6 


5 " 


6 " ....... 




h n a 


35 6 


8 " 




9 " 




" 15 " 


35 6 


" 30 " 


35 6 







158 



SURF AC li liOUILIBRIA 



of these substances in the circulation does not carry with it a fatal 
hemolysis of the red cells — in the case of jaundice, for instance — 
although present in sufficient quantities to lower considerably the sur- 



69 

67 

. 65 

J 63 

to 

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2 4 6 



6 10 12 14 16 18 20 22 24 26 28 30 
Time in -minutes 

Fig. 62. 



face tension of an equal volume of saline solution. * The antagonistic 
action of the plasma proteins counteracts the effect of the excess of 
bile salts and owing to this phenomenon of defense, the surface tension 
of the blood is not lowered to a dangerous degree. 



64 

62 
60 

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-»- glycerin 10 -per cent 
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2 4 6 8 10 12 14 16 15 20 22 24 26 26 30 
Time in minutes 

Fig. 63. 



Figures 62 and 63 express the results of similar experiments made 
with colloidal gold and traces of powdered sodium oleate. 

The mechanism of this phenomenon can best be explained by assum- 
ing that it is simply due to adsorption of the small molecules by the 



EQUILIBRIUM OF'COMPLEX COLLOIDAL SOLUTIONS 159 



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160 



SURFACE EQUILIBRIA 



large ones. An egg albumin molecule, for instance, may adsorb about 
160 sodium oleate molecules (assuming that adsorption takes place 
identically on the 6 faces of the albumin molecule). It may be pro- 
visionally admitted that the mean dimensions of the serum protein 
molecules are analogous to those of egg albumin. This being assumed, 
there are approximately 2.3 X 10 18 molecules in 2 cc. of serum. The 
amount of sodium oleate added is 0.0002 gm., which represents 37.4 X 
10 18 molecules, or more than 16 times as many. Each protein molecule 
may then adsorb 16 molecules of sodium oleate, and in this case the 
action of the oleate is entirely annihilated. The initial surface tension 
is not restored when the ratio of the number of molecules of each sort 



Dynes 



















































































































































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TitneO 12 3 4 5 



Fig. 65. — Rise of surface tension of pure serum and serum solutions after a drop 
due to the addition of sodium oleate. 



is equal to 1/160 (serum diluted to 1/20, sodium oleate to 1/10,000. 
Table XXIII). The antagonistic effect remains appreciable. The 
final surface equilibrium of such a complex solution of colloids is thus 
determined to a certain extent by the adsorption of one by the other. 

Gum arabic (Fig. 64), egg albumin, gelatin, gold and silver sols 
behave qualitatively in the same way when their solutions are placed 
in contact with strongly surface active substances. It is conceivable 
that this phenomenon could be used to determine the surface of adsorp- 
tion of these substances. 

The initial drop in surface tension is smaller when a solution of 
sodium oleate is used instead of the powdered substance. The two 
liquids mix readily and the adsorption, that is to say the neutralisation 
of part of the sodium oleate by the protein molecules, takes place before 
the sodium oleate molecules can reach the free surface. On the con- 
trary, when powder is used the molecules spread rapidly over the sur- 



EQUILIBRIUM OF COMPLEX COLLOIDAL SOLUTIONS 161 

face, and a considerable drop in the surface tension takes place instan- 
taneously, owing to the fact that they are largely in the superficial layer. 
(Fig. 61.) If the solution of sodium oleate be poured in and stirred, 
the results will differ from those obtained when the solution is carefully 
added drop by drop. 

Figures 65 and 66 express the results of two series of experiments 
conducted in a somewhat different way. In the first series, a constant 
amount of sodium oleate was added to different quantities of proteins, 

Dynes 
64 



62 
60 
58 
56 

54 
52 
50 
48 
46 
44 
42 
40 
38 
36 













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Y- 








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yoOj 








































































































































































































Vjfi 


10^ 








































J /5 













































34 
Time 12 3 4 5 



10 



15 



20min A 



Fig. 66. — Rise of surface tension of a 1/10 serum solution after the addition of 
different amounts of sodium oleate. 



while in the second series the amount of proteins was kept constant 
and the quantity of sodium oleate was varied. Serum was chosen 
rather than any other protein solution on account of its stability and 
the constancy of its characteristics with respect to surface tension, 
and sodium oleate was used because of its great activity. These two 
substances are typical and the results obtained may be observed quali- 
tatively with others. 

The curves in Figure 66 may be expressed by a formula of the form : 

y = a log. t + b, 
where a and b are constants. This is clearly to be deduced from Figure 
67 in which three of these curves were plotted on semi-logarithmic paper. 



162 



SURFACE EQUILIBRIA 



Figure 65 shows that when diluted to 1/10,000 the serum can no 
longer combat the action of 1/ 10,000th of sodium oleate. This is also 
generally true when 1/100 by weight of sodium oleate is added to pure 
serum. Serum diluted to 1/10, still keeps a certain antagonistic power 
when 1/500 or 1/1000 in weight of sodium oleate is added. 

As stated above, the manner in which sodium oleate is added to the 
serum is not unimportant. The results differ quantitatively when, for 
example, 1 drop of a 1/10 solution of sodium oleate is added instead 
of 10 drops of a solution at 1/100. Usually, the more concentrated the 
solution, the greater the antagonistic power of the pure serum. 



Rabbit Serum,Nal20 





























,« ***** 


ooo___^. 


















SerornJ^J. < 


























e 10-* , 


















SerumJ^^L 




















q e rum 1 


^jjjodJ^-3 

























































Fig. 67. — Rise of surface tension of a 1/10 serum solution after the addition of 
different amounts of sodium oleate (curves of Text — Fig. 66), plotted on 
semilogarithmic paper. 



Heat even at 55° modifies certain properties of the serum, but this 
alteration cannot be detected by the usual chemical and physical 
methods. This fact is well known biologically. The presence of 
a modification can, however, be demonstrated by the alteration in the 
aspect of NaCl crystals after evaporation of a serum solution at 
1/10 to which 1 : 10,000 of sodium oleate had been added. Plate II 
illustrates this point. The four photographs are of the same serum 
solution, unheated, heated at 56° for 2 hours, at 70° for 1 hour and 
boiled for 5 minutes. 

Figure 65 expresses the variation in the antagonistic property of 
serum heated at 56°. The phenomenon is more marked when a solu- 
tion of serum at 1/10 has been kept at 100° for 5 minutes. (Fig. 68.) 

Clark, Zinck and Evans 2 have observed that the protective action 
of human serum against hemolysis of guinea-pig red cells by sodium 
oleate was decreased after the serum had been boiled. In other words, 
they observed the same hemolysis with a smaller amount of sodium 

a H. Clark, R. H. Zinc and F. A. Evans, Bull. Johns Hopkins Hospital, 1921, 
XXXII, p. 32& 



EQUILIBRIUM OF COMPLEX COLLOIDAL SOLUTIONS 163 



oleate (1/50,000 with fresh serum; 1/65,000 with boiled serum). We 
were not able to reproduce the results of these experiments by using 
rabbit serum and chicken cells, but our curves show that the surface 
tension of boiled serum is inferior by 8 or 10 dynes to that of fresh 
serum, which in itself would account for a different behaviour. More- 
over, although the recovery is more rapid during the first 8 minutes 

Dynes 
62 



60 

58 

56- 

54 

52 

50 

48 

46 

44 

42 

40 

38 

36 

34 
Time 



1 




















































































1 






























-, rl ifl 


» 










jl 
























V 


fig 


ed^ 














ll 




























Bo 


jled 


5TT 


in. 








1 










































1 








^ 


































1 




/ 






































1 


/ 


f 






































I 


/ 










































I 










































i / 










































J 

















































































12 3 4 5 



10 



15 



20mia 

Fig. 68. — Rise of Surface Tension of a 1/10 Serum Solution Before and After 
Heating 5 Minutes at 100° C. 

(Figure 68), the equilibrium value was lower than that obtained with 
fresh serum. It may be, therefore, that the phenomenon depends on 
two factors: the initial value of the surface tension and a modification 
in the adsorbing power of the serum molecules. 

A Highly Sensitive Method for Detecting Proteins and Colloidal 
Particles in a Solution. 

A method for detecting traces of proteins, or any large molecules or 

micellar aggregations, was based on the above described phenomenon. 3 

Until now it has been generally believed that immunological reactions 

were the most sensitive, as they make it possible to detect such minute 

amounts as 0.000,000,05 gm. (5 X 10~ 8 gm.) of proteins in a sensitized 

guinea-pig. Wells, 4 in his excellent book on 'The Chemical Aspects 

'Lecomte du Noiiy. Science. 1925. LXI, p. 472. 

*H. G. Wells. The Chemical Aspects of Immunity. Am. Chem. Soc. Mono- 
graphs. 1924. 



164 



SURFACE EQUILIBRIA 



of Immunity, '' remarks that "these figures give a striking illustration 
of the delicacy of the immunological methods and their value in studying 
certain problems in protein chemistry. In no other way would such 
minute amounts of proteins be detected in a solution." 

Nevertheless, it is possible by a purely physical method to detect the 
presence of still smaller amounts of proteins; i.e. 0.000,000,02 gm. 
(2 X lO" 8 gm.) of albumin in 2 cc. of water, or 1/50,000,000 by weight. 
The results are quite constant. 

Under certain conditions, by using the concentration of sodium oleate 
corresponding to the formation of monolayers in our watch glasses, we 
succeeded in detecting as little as 1/100,000,000 (1 X 10" 8 gm.) and 
even 0.5 X 10~ 8 gm., in which case this method is ten times more sensi- 
tive than the most delicate of any of the biological methods. 

As the presence of 1 X 10 -6 gm. of proteins has no effect on the value 
of the surface tension of water (in the watch glasses), it was necessary 
to resort to an indirect method. Consequently, the so-called antago- 
nistic phenomenon was utilised in the following way: 

Measurements of the initial and static values of the surface tension 
of a highly diluted solution of pure sodium oleate are taken at an interval 
of two hours. The difference between the two readings is recorded. 
The same experiment is then repeated with a sodium oleat solution 
to which proteins, or colloids, have been added ; care being taken, of 
course, that the final concentration of sodium oleate is the same as in 
the first experiment. The sodium oleate molecules are adsorbed on the 
protein molecules and, being removed from the surface, no longer affect 
the static value of the surface tension. Table XXIV and Figure 69 
express the results of an experiment with the controls, pure water and 



TABLE XXIV. 
Surface Tension in Dynes. 



No. of Experiment 


Initial values 


Static values 
(2 hours) 




1 


2 


3 


1 


2 


3 


1. Water 


75.4 
75.1 
75.0 

75.0 


75.3 
75.1 
74.9 

75.0 


75.3 
75.2 
74.7 

75.0 


75.3 
75.3 
70.8 

75.1 
4.3 


75.3 
75.3 
72.0 

75.2 
3.2 


75 3 


2. Egg albumin crystal. 1/50,000,000.... 

3. Sodium oleate, 1/600,000 


75.3 
71.0 


4. Sodium oleate + egg albumin same 
concentrations as above 


75.2 


Difference between the static values 
of Sol. No. 3 and 4, due to the 
presence of egg albumin 


4.1 



EQUILIBRIUM OF COMPLEX COLLOIDAL SOLUTIONS 165 

pure albumin, using watch glasses with 2 cc. of liquid. The final dilu- 
tion of sodium oleate was 1/600,000 and that of egg albumin 
1/50,000,000. 

As has already been stated, the phenomenon is much more marked 
when a sodium oleate dilution at 1/750,000 is used; for, in spite of 



T6 



i=^r 



74 



72 



70 






•— • Wate* + efc§ albumin y50,000,000 
o— o w&tei* 

• — • Water> + sodium oleate V600.000 
o— -o Sodium oleate + eQg albumin 



Houps 



Fig. 69. 



the fact that the number of sodium oleate molecules is less, they can 
Organise in a monolayer, and the drop of surface tension in 2 hours is 
much greater (up to 20 odd dynes). Under these conditions, the 
presence of 1/100,000,000 (1 X 10~ 8 gm.) of albumin completely in- 
hibits the drop. But, as stated in Chapter 4, an exceptionally pure 
sample of sodium oleate is required to build up a monolayer. 



Chapter 9. 
Interfacial Tension. Surface Viscosity. 

Interfacial Tension. 

The surface tension at the surface of separation of two liquids is, 
from a biological point of view, of even greater interest than the surface 
tension of a liquid in contact with air. Indeed, all capillary effects in 
cells and organisms take place at the interfaces between liquids, tissues 
and gels. 

The measurement of interfacial tension has been rather difficult until 
now, as the method generally employed consisted of counting drops of 
one liquid falling into another. 

In spite of the difficulties, however, the work of Harkins and his 
collaborators 1 has thrown light on the behaviour of pure organic liquids. 
Prof. Harkins states that his "method is undoubtedly the most accurate 
of all those that have been devised, but it has given the most inaccurate 
results because the corrections which have been used by other workers 
than ourselves are incorrect." 2 

This authoritative opinion gives an idea of the reliability of the 
method. Our aim was to devise a method which, although far from 
claiming to be the most accurate, would, nevertheless, not require cor- 
rections so important as to render it inaccurate in the hands of others. 
For this purpose the instrument illustrated on Plate XVIII, Figure 1, 
the details of which are shown in Figure 70, was constructed. 3 

Our main purpose was to facilitate the study of adsorption phe- 
nomena at interfaces. This instrument gives both the dynamic and the 
static values of the surface tension as does the tensiometer from which 
it was evolved. It is simple and makes it possible to study rapidly and 
with great ease certain problems such as the action of temperature. 

The instrument consists of a tensiometer, modified so that the plati- 
num ring may be pressed down vertically, while its plane remains 

X W. D. Harkins, F. E. Brown & E. C. H. Davies, J. Am. Chem. Soc. 1917, 
XXXIX, p. 356. 

2 W. D. Harkins & W. C. Cheng, J. Am. Chem. Soc. 1921, XLIII, p. 35. 
3 Lecomte du Noiiy, J. Gen. Physiol. 1925, VII, p. 625. 

166 




Fig. 1. 




Fig. 2. 
EXPLANATION OF PLATE XVIII. 

Fig. 1. — Interfacial Tensiometer, with 6 cm. ring. 

Fig. 2. — Appearance of the interface between water (top) and carbon tetra- 
chloride (below) when the ring is pressed down. Picture taken just before 
breaking, in the state of equilibrium. 

167 



168 



SURFACE EQUILIBRIA 



horizontal. It was necessary, therefore, to attach the ring to a rigidj 
support, kept in its perpendicular position by means of an articulated 
parallelogram. According to whether the vernier is moved clockwise 
or counter-clockwise, the ring will be pressed down or pulled up. It is 
pressed down when water has the lower density of the two liquids used 
and pulled up in the opposite case. Figure 2, Plate XVIII, shows the 
appearance of the interface between water and carbon tetrachloride. 




Fig. 70. — Design of the Interfacial Tensiometer. Dimensions are in millimetres. 



The scale is graduated throughout the circumference of the dial. The 
length of both horizontal arms can be adjusted so as to change the 
momentum of the force applied to the ring and to make the instrument 
direct reading. The ring itself (4, 6, 8 or 12 cm. in circumference) 
is fixed on a light, brass stem, threaded so that one single turn is suffi- 
cient to attach it rigidly to the support. The balance of the whole 
moving system is roughly obtained by a counterweight, and the finer 
adjustment of the zero is realised, as in the ordinary tensiometer, by 
twisting more or less the end of the torsion wire. 



INTERFACIAL TENSION. SURFACE VISCOSITY 169 



~Y~ (see Chapter 1). When this is 



The instrument is standardised with weights in the usual way by 

application of the formula y 

done it is, of course, adjusted not only for upward pull but also for 
downward thrust, and the readings are identical in both ways. 

All readings are made at the zero position of the arm, by raising or 
lowering the table supporting the two liquids, or the instrument itself. 
A thin index, attached to the lower arm, moves on a white background 
supported by the frame. On this background, a raised black mark indi- 
cates the position of horizontality when the index exactly faces it. As 
the mark and the index are in the same vertical plane, no parallactic 
error can occur in this determination. Two movable stops limit the 
swing of the arm. 



TABLE XXV. 

Surface Tension and Interfacial Tension against Water. 



1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

13 

14 

IS 

16 

17 

18 
19 
20 
21 
22 



Chloroform 

Isoamyl alcohol 

Octyl alcohol . . 

Benzyl alcohol . 

Ethyl iodide . . . 
ether 
phthalate 
carbonate 
acid 



Ethyl 
Ethyl 
Ethyl 
Oleic 

Benzene 

Toluene 

ra-xylene 

Castor oil 

Olive oil 

Dimethyl aniline 
Diethyl aniline . 
Turpentine 



Liquid 



"Non-spreading 
liquids," accord- 
ing to Harkins. 



Carbon bisulfide 

Paraffin oil 

Carbon tetrachloride 

Bromof orm 

Liquid petrolatum Squibbs, 



°C. 
25.0 
23.5 
25.0 
25.0 
25.0 
23.0 
25.0 
25.0 
25.0 
25.0 
25.0 
23.0 
23.0 
23.0 
26.0 
25.0 
25.0 



20.0 
25.0 
23.0 
25.0 
24.0 



27.5 
24.2 
28.6 
43.3 
32.3 
18.0 
40.8 
29.0 
34.2 
29.0 
28.0 
30.0 
36.4 
33.0 
38.4 
35.4 
29.2 



34.0 
32.0 
28.0 
39.5 
33.0 



e s 

o >- 



.2 £ 
u 

u c 

-l_i TO 

G be 

t— i rt 



27.9 
4.4 
10.8 
4.8 
36.6 
10.9 
16.4 
11.9 
12.8 
32.3 
32.5 
35.0 
15.4 
17.0 
21.0 
21.3 
13.7 



33.8 
47.0 
40.0 
27.5 
49.0 



+ 0.4 
-19.8 
17.8 
-38.5 
+ 4.3 

- 7.1 
24.4 
18.1 
21.4 

- 1.3 
+ 4.5 
-f- 5.0 

21.0 
16.0 

-18.9 
14.1 

-15.5 



0.2 
f 15.0 
+ 12.0 
-12.0 
+ 16.0 



Ih 

SO 

ci 
m 



1.526 
0.825 
0.837 
1.023 
1.944 
0.718 
1.126 
0.978 
0.708 
0.880 
0.882 
0.878 
0.950 

0.955 



1.259 
0.850 
1.608 



170 



SURF/ICE EQUILIBRIA 





.S 
•a 

<u 

Ih 

04 
to 
1 

a 




S3 


49.0 

55.32 






CM 


27.5 
40.85 




8 


37.2 
52.63 




ON 







OO 


33.8 

54.09 

37.4 




10 


21.0 
25.78 




Tf 


17.0 
18.2 




13 

15.4 
22.63 


n 

< 

> 

< 

< 


CM 


35.0 
37.6 


i-H 


32.5 
36.10 


O 


32.3 
34.97 


l-H 


Ox 


00 10 
cm »r> 




00 


11.9 

12.86 


0. 


16.4 
16.27 




VO 


2 


< 

Oh 

o 


lO 


36.6 
40.02 


(J 


Tf 


4.8 

4.75 




CO 


10.8 
8.52 




CM 


4.4 
4.42 




1— 1 


27.9 
27.7 




S a} 

"EH 
a 
Pi 

<3 




Tensiometer (du 
Nouy) 

Drop method (Har- 
kins) 

Cathetometer 

(Quincke") 


t 



INTERFACIAL TENSION. SURFACE VISCOSITY 171 

Table XXV gives the results obtained with a number of substances. 
No attempt was made to secure other than commercial C. P. liquids, 
our only aim being to check the soundness of the method. As Harkins 
and his collaborators took especial pains to obtain absolutely pure ma- 
terials, the discrepancies found between their values and the tenso- 
metric values may be accounted for in this way, so far as the substances 
spreading on water are concerned. (Table XXVI.) However, the 
values disagree for the liquids which do not spread on water, i.e. those 
having an interfacial tension greater than the difference between the 
surface tension of water and that of the liquid. (For example, paraffin 
oil, S.T. = 32 dynes, difference from water 42.2 dynes. Interfacial 
tension in contact with water 47 dynes.) 4 In this case no tension is 
greater than that of the other two and a triangle of forces is possible 
and real. 

Without questioning the accuracy of Harkins' semi-dynamic values 
for the interfacial tensions between water and this special class of sub- 
stances, it might be pointed out that Quincke, 5 using a static method 
(cathetometer), gave for the interfacial tension water — CS 2 the value 
of 37.6 dynes, while we obtain 33.8 dynes and Harkins 54.09 dynes. 
The difference between the value given by Harkins and those of 
Quincke and ourselves, is probably due to the fact that Harkins meas- 
ures the value of the dynamic tension while we measure the static value. 
The action of temperature is particularly interesting. It is known 
that the surface tension of all liquids in contact with air decreases when 
the temperature rises. When two liquids are in contact, however, their 
interfacial tension is often independent of the temperature, between 
certain limits, .and sometimes even increases, contrary to what occurs 
in a free surface. Table XXVII and Figure 71 give the results ob- 
tained with ethyl ether and carbon disulfide in contact with water. 
Harkins observed the same phenomenon with octyl alcohol, heptalde- 
hyde and heptine, but does not mention ether or carbon disulfide. 
Measurements became impossible for the latter at temperatures above 
35° on account of the continual formation of bubbles at the interface. 

A ring with a circumference of 6 cm. was generally used for these 
measurements, but we often used one of 12 cm. for the very low values 
(water — benzyl alcohol = 4.8 dynes, water — iso-amyl alcohol = 4.4 
dynes, etc.) Owing to the mutual solubility of these latter substances, 

4 This distinction between the two kinds of liquids established by Harkins, does 
not correspond to any definite chemical characteristic of the molecules. 

*M. G. Quincke, Phil. Mag. 1871, XLI, ser. 4, p. 245; and Chwolson, Traite 
de Physique, Paris, 1907, I, p. 631. 



172 



SURFACE EQUILIBRIA 



w 
H 

> u 

x g 
X fa 



s 


CM 
CM* 


in 

CO 


O 
vd 

CO 


On 


o 

«0 


CO 


t>. 


CM 


VO 
CO 


CM 


«o 
cm 


CO 
CO 


CM 
CM 


CM 
CO 


CM 


On 

CO 
CO 


ON 

o 


8 


oo 

CO 

CO 


On 

1—1 


lO 

CO* 

CO 


VO 

o 


tX 


l-O 

CO 

CO 


o 


VO 


CO* 
CO 


to 

1— 1 


p 

CO 

CO 


co 

o 


Tf 


o 
cm' 

CO 


o 
o 


CO 


CO 


CM 


CO 


On 


- 


io 
CO 


o 


p 

CO 


ON 


p 

CO 


io 

ON 


00 


On 

O 
co 


lO 

On' 



c • c - 



.2 • o_ 

CO qj CO <U 

«- rt Vh rt 

c c 



INTERFACIAL TENSION. SURFACE VISCOSITY 173 

the interfacial tension is not really measured between pure liquids but 
between two liquids saturated by each other. 

To give an idea of the difference in rapidity of the two methods 
(drop and ring method) it suffices to point out that to measure the 
tension, water-benzyl alcohol, about 800 drops of benzyl alcohol in water 
will have to be counted, if the surface tension of water be determined 
by counting 50 drops. It is generally admitted that to get precise 
measurements the drop must form slowly, thirty seconds being a mini- 
mum and two minutes an optimum for the formation of each drop. 
This gives 25 minutes for the measurement of the surface tension of 



Dynes 




36 


c 


35 


o 




no 




S 


34 


4-> 




3 


33 


a 




V— 




& 


VI 



- 31 



30 



w< 


vtep- 


CS 2 




































































i 


1 


\^**^ 




















< 


• 


< 


i^*"" 


















































^9^ i 


• 





















































































29 

T* 8° 10° 12° 14° 16° 18° 20° 22° 24° 26° 28° 30° 3£° 35 # 

Fig. 71. — Interfacial Tensions of Water-Carbon disulfide interface, as a function 

of temperature. 



pure water and a little over 6^ hours for that of the interfacial tension 
between the two liquids. With the tensiometer, the measurements 
require respectively 30 seconds and 1 minute; the difference being due 
to the fact that when interfacial tensions are measured, it is preferable 
to increase the torsion of the wire slowly. 

It sometimes happens with certain liquids, paraffin oil, for instance, 
that, owing to an irregularity in the ring, or its lack of horizontality, 
the tearing of the film is not produced abruptly on its entire circum- 
ference. It is then necessary to correct the fault as much as possible 
and to repeat the measurements until a concordant series of values is 
obtained. It is preferable to immerse the ring in the water and to 
make the measurement in the direction water — > liquid, rather than 
liquid -* water. The values obtained in the two cases are sometimes 



174 



SURFACE EQUILIBRIA 



equal but are more often too low when the ring passes from the other 
liquid to the water. However, the readings check perfectly even when 
the ring has passed through oil before reaching the surface of the water. 
The important problem of adsorption at interfaces as a function of 
time can easily be studied with this instrument as shown by Figure 72, 
which expresses the phenomenon of adsorption of sodium oleate by 
paraffin oil. It will be seen at a glance that the same delayed phe- 

3Z 



& 40 



4Q3 

3S.7 



37.2 
366 



34.1 
32.5 



MJO 



I 


38 
36 


3 2as 
|zra 




34 


264 




32 


248 




30 


23.3 




28 


21.7 




26 


201 



24 188 




16ftna. 



20 40 60 • 20 40 60 : 20 40 60 » 20 40 60 • 20 40 60 ■ 20 40 60 • 20 40 
ihi> 2hi»s. 8hps. 4h-r»3. 5hps. 6hi»a. 

Time 

F|7. 72.— Adsorption Isotherms of Sodium Oleate— Paraffin oil, 22°. The inter- 
w?^^5i 0ns a£ re P Iotted against the time, Concentrations 1/10,000, 1/100,000, 
1/1,000,000. Ihe upper curve expresses the interfacial tension between pure 
water and paraffin oil. It will be seen that it also decreases as a function of 
time, on account of the slight solubility of the oil. After 24 hours standing 
the value of the Interfacial Tension Water; P. Oil was 30.3 dynes; after 48 
hours, 28.4 dynes; after 64 hours, 28.3 dynes. The equilibrium is prac- 
tically reached after 64 hours. Vessels were 10 cm. in diameter ; 100 cc. of oil 
and 100 cc. of solution were used. 

nomenon which was found to occur at the free surface of a colloidal 
solution also occurs at interfaces as was expected and that it can be 
studied quantitatively with great accuracy. 

* 

* * 



Surface Viscosity. 

The surface viscosity conceived as indicated below of a colloidal solu- 
tion evidently increases as a function of the time as the molecules in 



INTERFACIAL TENSION. SURFACE VISCOSITY 175 

solution are adsorbed in the free surface of the solvent. This fact was 
easy to foresee. 

Our aim was to measure a quantity which, even though not actually 
the viscosity itself, we shall designate by that name for lack of a better 
one. The micro-viscosimeter described in 1923 6 was altered for this 
purpose in the following way. 7 

A small, glass rod, 0.4 mm. in diameter and 10 mm. long, was hori- 
zontally attached by means of shellac to a vertical, brass rod and hooked 
to the galvanometer wire (Leeds & Northrup rolled phosphor bronze, 
0.00125 mm. thick = 0.002 inch) instead of the cylinder. The whole 
system could be brought in contact with the surface of the liquid by 
means of a rack and pinion device. A mirror permitted readings 
on a scale and a light damping device provided a steady spot. The 
solution was poured into a watch glass, or any other vessel, and placed 
on a stand which could be slowly rotated ,by a motor at constant speed. 
When the instrument is used as a viscosimeter, the motor drives the 
vertical shaft at a speed which can be varied by means of pulleys of 
known ratios, from 3 up to 36 revolutions a minute or more. But for 
the measurement of surface viscosity, as we will call it, it was necessary 
to proceed differently. Real viscosity, indeed, is no longer in question, 
but the resistance to the tearing which characterises the adsorbed film. 
It is possible that, in certain cases, the molecules glide over one another, 
but such is not usually the case, for there is a semi-solid or solid film 
at the surface. At certain concentrations there is a sort of reticular 
structure (monolayer). It is even probable that what we measure is, 
in certain cases, the rigidity of a film combining these characteristics. 
Now the interest, so far as we are concerned, lay in following the 
formation of the film step by step. It was thus essential not to destroy 
it each time. With this object in view, the motor was demultiplied 
until the vessel containing the liquid accomplished only 2 or 4 revolu- 
tions in an hour, or 360° in 30 or 15 minutes. Thus, in the latter case, 
the rotation of the glass was a little more than 23° per minute. The 
scale was placed at such a distance that the angle of 23° had an aperture 
of about 50 cm., or 500 divisions. By letting the motor revolve during 
exactly 1 minute, assuming that the suspension wire was rigidly attached 
to it, the spot traveled up the whole scale. 

Each measurement was made in the following manner. The contact 
between the horizontal glass rod and the liquid being established, the 

"Lecomte du Noiiy, J. Gen. Physiol. 1923, V, p. 249. 
7 Lecomte du Noiiy, Science, 1925, LXI, p. 117. 



176 



SURFACE EQUILIBRIA 



motor was allowed to turn during 1 minute. The current was auto- 
matically shut off at the end of that time by clock-work. The reading 
was made by taking the highest value reached on the scale by the spot. 
For a serum solution at 1/10,000 corresponding to a concentration of 
the proteins of about 1/160,000, the surface rigidity in the beginning 
was as can be seen in Table XXVIII. Then, as the molecules are 



TABLE XXVIII. 

Variations in Function of the Time of the Surface Viscosity of a Serum 
Solution at 1/10,000 Temperature = 22° C. 



Time in minutes 





7 


10 


15 


30 


50 


90 






Readings (proportional to the vis- 
cosity) 





27 


40 


55 


104 


170 


284 







adsorbed in the surface layer, the rigidity increases during the first 
40 minutes almost proportionally to the time. (Fig. 73.) 

oOO 

280 

260 

240 

220 



160 



<q 200 

oo 

I 

S 160 

^o 120 
*> 100 

ao 

60 
40 
20 


Min.O 















r 


Uc 




Surface viscosity 






7 


















































































/ 


















/ 


















t 
















































/ 


















/ 
















/ 


















L 



















10 20 30 40 50 60 TO 60 90 
Time 

Fig. 73. 



At the end of 1 hour and 30 minutes, the rigidity has become consid- 
erable, almost 300 times greater than at the beginning of the experiment ; 
although the thickness of the adsorbed layer is only of the order of 
magnitude of 40 X 10~ 8 cm. (see Chapter 3). For these experiments 



INTERFACIAL TENSION. SURFACE VISCOSITY 177 

the solution was placed in a watch glass, the dimensions of which were 
such that a monolayer could form. 

In certain cases the film is perfectly elastic. This fact is put in 
evidence by the return of the spot to 0, as soon as the motor is stopped. 
In other cases a tearing is produced and the spot can no longer go 
back to 0. 



Chapter 10. 

Colloidality of Solutions of Proteins, Serum and 

Plasma. 

The colloids in general are often negatively described as being devoid 
of the principal properties characterising the crystalloids. There seems 
to have been insufficient emphasis on the fundamental differences be- 
tween substances known as typical colloids and those existing in the 
colloidal state only under special conditions. 

The term colloid is too general and is often misleading. A whole 
chemistry of colloids was originated in Germany. A number of the 
most eminent scientists, among whom was the great and deeply regretted 
Jacques Loeb, protested energetically against such an unnecessary 
classification. 

By his admirable experiments, Jacques Loeb succeeded in showing 
that, in many cases, there is no unbridgeable gap between classical 
chemistry and colloid chemistry, and that it was only because the ex- 
periments had not been made under the proper conditions that the 
stoichiometric laws had been found inapplicable to such colloids as 
gelatin, for instance. 

A number of scientists look upon the colloidal state as being essen- 
tially characterised by the aggregation of molecules in the shape of 
"micellae." Visual proof of their existence has been given by the ultra- 
microscope. The Brownian movement cannot be questioned. Elec- 
trically prepared metallic sols are put in the same class with such 
substances as albumin because both have a certain number of properties 
in common : ultra-microscopic appearance, non-dialysability, etc. 

These substances are, however, fundamentally too dissimilar to justify 
their being put under the same heading. Albumin being classified as 
a typical colloid, is naturally expected to form a colloidal solution in 
water. The idea that free albumin molecules could exist in the solvent 
and form a true solution was never considered until very recently, 
although micellae-free solutions had been observed. 1 A great deal of 

1 "Soluble starch and crystallised albumin . . . although they show a light 
cone (Tyndall cone), their individual particles cannot be distinguished but prob- 

178 



SOLUTIONS OF PROTEINS, SERUM AND PLASMA 179 

confusion has resulted from this arbitrary classification, and Graham, 
who knew of the intermediate states of matter, would have been sur- 
prised at some of the consequences of his terminology. 

Let us consider the most important substances in biology : the pro- 
teins. Their main physico-chemical characteristics are: non-dialyza- 
bility, the Brownian movement, the tendency to coagulate or to 
precipitate under various influences. None of these properties is 
essentially specific of the proteins nor of colloids in general. 

It is true that the Brownian movement, or rather the visibility of 
the ultra-microscopic particles agitated by molecular activity, is due 
to the presence of molecular aggregates of a certain size, but it is 
not at all certain that the non-dialyzability is due to the same cause. 
As a matter of fact, the dimension of the single albumin molecule 
deduced from the experiments of Sorensen, Cohn and Lecomte du Noiiy, 
are of such an order of magnitude as to prevent its passing through 
the pores of the dialyzer, even though these are not narrowed by 
adsorption on their walls. Thus it is evident that egg albumin, even in 
true solution, might not dialyze. 

On the other hand, the individual egg albumin molecules cannot be 
seen on the dark field, in spite of their enormous size, of the order of 40 
angstroms. Consequently, it must be admitted that a certain number of 
molecules in a given solution are agglomerated as micellae. The diam- 
eter of the smallest visible particles is of the order of 60 angstroms (gold, 
60 X 10 -8 cm. 2 Such a diffracting micella could be formed of 8 mole- 
ably are about 5u|T (50 X 10" 8 cm.). R. Zsigmondy. Colloids and the Ultra- 
microscope, trans, by J. Alexander, 1st Ed. Wiley, 1909, pp. 4 and 88. 

2 "A particle the size of a starch molecule can, within its own mass diffract 
light of sufficient intensity to be observed" (Lobry de Bruyn. Rec. Trav. Chim. 
Pays Bas, 1900, XIX, p. 251. See also 1904, XXIII, pp. 155 & 218). Also 
quoted by Zsigmondy, loc. cit., p. 88. This does not mean, however, that indi- 
vidual molecules of such order of magnitude (which is that of the elements of 
serum and of egg albumin), could actually be seen as ultra-microscopic particles, 
as the index of refraction of these substances has to be considered. But the 
light cone of such solutions could very well be due to the presence of free 
molecules, and it is unnecessary to assume their aggregation in micellar form. 
An analogous observation is found in Zsigmondy's "Chemistry of Colloids," 
translated by Spear. (Wiley, N. Y., 1917, p. 236.) After reaching the con- 
clusion that the diameter of the hemoglobin molecule is probably 2.3 to 2.5^u., or 
23 X 10" a cm. (taking 16,000 for its molecular weight), he remarks, "It is 
worthy of note that the determinations of the diameter of amicrons in gold 
solutions have given values similar to the above." (Zeits. f. Phys. Chem. 1906, 
LVI, p. 65.) At present there is a strong tendency to admit a higher molecular 
weight, around 64.000, for hemoglobin. This would bring the diameter of the 
molecule to about 40 X 10" 8 cm. 

The bibliography of light diffraction by the molecules of liquids and gases 
up to 1921 was published by W. H. Martin, in Trans. Roy. Soc. Canada, 1922, 
XVI, p. 276. Some of the most interesting papers on the subject are: W. H. 



ISO SURFACE EQUILIBRIA 

cules joined together in the shape of a parallelopiped (60 X 60 X 41 
angstroms). Two thousand aggregated molecules would result in a 
particle having a mean diameter of 400 angstroms, comparable to those 
of colloidal silver and platinum. There is, however, no serious reason 
for assuming that all the molecules in a protein solution are grouped 
in such a way, while there are a good many reasons, on the contrary, 
for believing that these aggregates represent only a certain percentage 
of the molecules in solution. An equilibrium probably exists between 
the grouped molecules and the free molecules, and the relative propor- 
tion of the two evidently depends on certain factors, such as dilution 
and hydrogen ion concentration. Sugar solutions, which have always 
been considered as typical, true solutions, show a very striking and 
brilliant Brownian movement under the ultra-microscope. Instan- 
taneous photographs of a 20 per cent solution of sugar, unfiltered and 
filtered through a Berkef eld candle, and fresh chicken plasma and serum, 
are reproduced in Plates XIX to XXII. The typical crystalloidal solu- 
tion, unless special precautions are taken, obviously resembles the typical 
colloidal solution, and it is clearly impossible to differentiate them on 
the basis of such a test. 

This sugar solution behaves normally as far as osmotic pressure is 
concerned. No objection can, therefore, logically be made to Sorensen's 
measurements of the osmotic pressure of albumin solutions. The agree- 
ment of his determination of the molecular weight of egg albumin using 
relatively concentrated solutions, with ours, obtained with highly diluted 
solutions, seems to indicate that in both cases the molecules were in 
the same state of aggregation. This affords an argument in favor of 
the aforementioned assumption that in certain colloidal solutions only a 
small number of molecules are aggregated as micellae, while the great 
majority exist as free molecules. 

This view is supported by other experimental facts. For instance, 
the organization of monolayers is only possible with free molecules 
capable of organization in the surface layer. (Sodium oleate, egg 
albumin, serum.) Solutions containing only micellae and a negligible 
amount of free molecules (metallic pseudo-solutions, sols, suspensoids) 

Martin and S. Lehrman. J. Phys. Chem. 1920, XXIV, 478; 1922, XXVI, p. 
75 ; 1923, XXVII, p. 558. F. B. Kenrick. J. Phys. Chem. 1922, XXVI, p. 72. 
H. W. Martin, Trans. Roy. Soc. Canada, 1923, XXVII, p. 151. 

All the work done on light scattering by molecules or particles is based on 
the fundamental work of Lord Rayleigh : Phil. Mag. 1871, XLI, pp. 107, 274, 
447; 1881, XII, p. 86; 1899, XLVII, p. 375. 

Important contributions to this subject were made by Cabannes — see bibliog- 
raphy listed above. 




Plate XIX. — Plasma (chicken) pure. Dark ground, Zeiss paraboloid condenser. 




Plate XX. — Serum (rabbit) pure. Dark ground, Zeiss paraboloid condenser. 

« 
181 




Plate XXL— Sugar solution (glucose), 20 per cent unfiltered. Dark ground, 
Zeiss paraboloid condenser. 




Plate XXII. — Sugar solution (glucose), 20 per cent filtered through Berkefeld 

filter. Darkfield, Zeiss paraboloid condenser. 

182 



SOLUTIONS OF PROTEINS, SERUM AND PLASMA 183 

never show minima of the value of the surface tension corresponding 
to a critical concentration in a given vessel. The drop in surface ten- 
sion, as a function of the time, is generally slight. 

The fact that we were able to estimate the thickness of the layer 
adsorbed on the red cells, by means of reasoning based on the ex- 
istence of free molecules in the plasma, and that this estimation was 
confirmed quantitatively by the direct measurements of Fricke, as well 
as all the unquestioned experiments of Loeb and Sorensen are added 
proof that under given conditions protein solutions should be considered 
as true solutions. This term is here taken in the sense of a solution 
containing free molecules but does not carry with it any assumption 
concerning their possible state of dissociation. 

It is, nevertheless, probable that most of these solutions only remain 
as true solutions for a short period of time unless special precautions 
are taken to prevent any physical alteration or any chemical reaction 
from taking place. A change in the pH concentration, the presence 
of C0 2 in the atmosphere, stirring, and many other causes, tend to 
upset the equilibrium and to increase the proportion of micellae. Serum 
generally shows a marked increase in their number after 24 hours stand- 
ing. A clear solution of sodium oleate at 1/1,000 will become opalescent 
in a few days, unless it is kept sealed under nitrogen. 

As far as living organisms are concerned, there is no way of proving 
that micellae exist in the plasma. At any rate, their number must be 
extremely small with respect to the free molecules. The conditions in 
which serum is placed when being studied are entirely different from 
those in the circulation. The influence of centrifugation and of the con- 
tact with the glass cannot be estimated. One fact stands out : perfectly 
fresh serum or plasma, examined under the ultra-microscope 30 minutes 
after the bleeding, shows the presence of to 3 micellae in a volume of 
1372 X 10- 12 cc. which contains 16 X 10 8 molecules (1 billion 600 
millions). Assuming that these micellae contain as many as 1600 mole- 
cules and that their diameter therefore is 50 \i\i, which is obviously 
exaggerated, 3 the ratio between the number of free molecules and the 

3 H. Bechhold and L. Villa, in the Bioch. Ztsch. 1925, CLXV, p. 257, state 
that "Jeder von uns gesehenen und gezahlten Lichtpunkte besteht aus' etwa 
funfzig physikalischen albumin Molekeln." In this case the ratio: 

No. of free molecules 



No. of aggregated molecules 



would be 10 millions. Only one molecule out of every 10,000,000 would be aggre- 
gated. See also footnote 1, p. 178. 



184 SURFACE EQUILIBRIA 

number of aggregated molecules would be — — ' ' = 333,333 

4,oUU 

in the case when three micellae are present permanently. This means 

that only one molecule out of every 333,333 takes part in building up 

the visible ultra microscopic particles. Less than 3 micellae in the 

above defined volume is frequently observed. It is probable that if the 

plasma were not handled at all, there would be none. Some plasmas, 

though handled, showed no micellae. The plasma was gathered in 

paraffined tubes kept at 0°. Tables XXIX and XXX, give the result 

of four series of observations. 

Blood plasma and blood serum cannot, therefore, be considered as 
colloids in the sense of pseudo-solutions composed solely of molecular 
aggregates. 

It thus seems rash, to say the least, to speak of "colloidoclasie" as 
does a certain school of French medical men, whose publications in this 
respect have been sometimes critically received in other countries. 4 The 
micellar aggregation in the blood fluid is probably one of the per- 
ceptible consequences of underlying physico-chemical reactions. Any 
lesion, any intoxication of the organism, determines a cellular perturba- 
tion, the origin of which is to be looked for in a chemical reaction of 
certain proteins. Unfortunately our chemical methods of analysis have 
not as yet led to a clear conception of the structure of the protein mole- 
cule. But it is wrong, or at least premature, to ascribe the pathological 
reactions observed clinically, or on experimental animals, and due to 
anaphylactic or peptonic shock, for instance, to a disturbance in the 
colloidal equilibrium of the proteins; for this disturbance may be 
nothing else than another consequence of a physico-chemical nature, of 

4 "French investigators particularly have attempted to explain the manifesta- 
tions of anaphylaxis as due to a disturbance in the colloidal equilibrium, with 
partial flocculation of the plasma colloids and, possibly, of those of the tissues 
themselves. They refer to this supposed change as "colloidoclasie" and have 
developed numerous explanations of the phenomena of allergy and anaphylaxis, 
as well as many proposed methods of treatment based upon this hypothesis. The 
literature in this field cannot be followed by one familiar with modern American, 
English and German work, for no careful distinction is made between ana- 
phylactoid manifestations and true anaphylaxis ; between specific desensitisation 
and non-specific reduction of irritability ; between anaphylatoxin effects and 
specific antigen-antibody reactions ; moreover, capillary thrombosis and pul- 
monary embolism are never ruled out or even taken into consideration {e.g., 
according to Lumiere, there is no difference between the effect of injections of 
suspensions of BaSO* and true anaphylactic shock). None of the modern work 
with muscle preparation in vitro; which rule out the factor of capillary occlu- 
sion, seem ever to be taken into account. Therefore we cannot discuss this 
phase of anaphylaxis at the present time, for the evidence presented is for the 
most part too glaringly inconsistent with known but disregarded facts." H. G. 
Wells, Chemical Aspects of Immunity, Am. Chem. Soc. Monographs, 1925, p. 211. 



SOLUTIONS OF PROTEINS, SERUM AND PLASMA 185 

TABLE XXIX. 



These readings were taken _ with a Zsigmondy slit ultra-microscope (Zeiss). 
The slit was set so as to illuminate laterally a layer of liquid 7y, thick. The 
width of the narrow part of the light cone observed in the microscope was 
equal to 42u.. The eye piece micrometer is divided into 18 squares, the sides of 
which are 7\i long. In the following table the number of particles occurring 
in 4 of these squares was counted. Hence, they were seen in a volume of 
the solutions equal to 14 X 14 X 7\i = 1372^ or 1372 X 10" 12 cc. Observations 
were made approximately every 30 seconds or every minute over periods of 
one hour. Three experiments in which particles were present are reported here. 
(Chicken plasma.) 

f 12336451351503623354323123221 
301203114560123342351232032232 
120135242335032533442023354123 

( 12332 1133. 

Number of obs. : 97. Mean value : 2.6 

f 344211003523645134431323214511 
\ 13434 11222342420 4347 433 6783 45 2 
[ 456035235724313 4. 

Number of obs.: 76. Mean value: 3.1 

12101100121102212300000121340222 
00111112012320423211310111101241 
02223541032 2. 

Number of obs.: 76. Mean value: 1.4 



Number of particles 

observed 
Expt. No. 1 



Expt. No. 2 



Expt. No. 3 



TABLE XXX. 

Number of Visible Ultramicroscopic Particles in Fresh Chicken Plasma. 
Same Conditions as in Table XXIX. 



Chick, plasma 
Fresh, 1st sample 



Same plasma 
2nd sample 



Same plasma JO 

3rd sample |0 1 



Same plasma 
4th sample 



Same plasma 
5th sample 



Same plasma. 
Samples changed after 
each reading (24 samples) 



00000 1111000001 
121211000000000 
000011000000111 
11100000000000 
Time: 1 minute. 76 readings. Mean value: 0.35. 

111222222111110 

000000000000000 

110000000000000 

Time: 1 minute. 60 readings. Mean value: 0.45. 

000000101000110 

000001111111100 

000000001111111 

Time: 1 minute. 60 readings. Mean value: 0.38. 

000000000000000 
001111101111111 
000000100000000 
Time: 1 minute. 60 readings. Mean value: 0.30. 

012111112333332 
110000000000000 
100000000000000 

Time: 1 minute. 60 readings. Mean value: 0.68. 






111 





111 






10 1 








000201000010 

10 02 1 00 1 

Time: 2 hours, one reading every 5 minutes = 24 readings. 

Mean value: 0.37. 

Mean of all experiments: 0.42. 



a chemical change in the proteins, as suggested above. In other words, 
these two phenomena, pathological and physico-chemical, may have the 



186 SURFACE EQUILIBRIA 

same origin, may be two manifestations of the same cause, but can, 
under no circumstances, owing to the absolute lack of direct proof, be 
considered as deriving from one another. There is no more reason for 
stating that the colloidal disturbance is the cause of the pathological 
trouble, than for stating that the pathological trouble is the cause 
of the colloidal disturbance. It is even quite probable that the proteins 
in the circulation were not in the colloidal state before the experiment. 
There is strong experimental evidence to this effect, as has been pre- 
viously pointed out. 

Moreover, "colloidal equilibrium of proteins" is a vague expression 
which needs to be defined. It would be most interesting to prove that 
such an equilibrium exists, as it would establish an important distinction 
between colloids and crystalloids. There is little doubt that this was 
one of the aims of the aforementioned school. Considering the gen- 
erous use that the head of this school and his collaborators make of this 
term, it is to be hoped that their researches have led them to important 
discoveries, which, however, they have thus far refrained from 
publishing. 

Auguste Lumiere for a long time defended similar views. His book 
"Role des colloides chez les etres vivants," published in 1921, expounded 
the most thoroughly "colloidal" ideas; but since that date, a number of 
important papers have been published, notably those of Loeb and Soren- 
sen, and, having read them, Lumiere, with his scrupulous scientific 
conscience, did not hesitate to publish an excellent article reversing his 
former opinions. 5 

The physico-chemistry of proteins is advancing. The important 
work accomplished in America, Denmark, Germany and England, has 
opened up a new field. In the United States the discoveries of Loeb, 6 
the important work of his collaborators, Northrup and Hitchcock, 7 
and the papers of Cohn, 8 have thrown much light on those problems. 

6 Auguste Lumiere, La Science Moderne, 1926, III, p. 10. 
* Jacques Loeb, Proteins and Colloidal Behavior, New York. 
7 D. Hitchcock, Physiol. Rev., 1924, IV, p. 505 (Bibliog.). 
8 E. J. Cohn, Physiol. Rev., 1925, V, p. 349 (Bibliog.). 



Chapter n. 
General Conclusions. 

It may be of interest to examine the experimental data recorded in 
this book from a thermodynamical and biological standpoint. 1 

The writer wishes to emphasize the fact that the following consid- 
erations are of a purely speculative nature. They seem, however, to be 
the natural deduction of the foregoing experimental work and may 
have already dawned on the reader's mind. 

It is impossible not to be impressed by the striking generality of this 
fact: all living matter is primarily composed of substances which con- 
siderably decrease the static value of the surface tension of water in 
which they are in solution in the living organisms. 

The Gibbs-Thomson's thermodynamic formula states that if a sub- 
stance in solution can decrease the surface tension of the solvent, it will 
concentrate at interfaces in such a way that the final equilibrium of the 
system will correspond to the minimum of free energy compatible with 
its total energy. On the other hand, the works of Gibbs and of Boltz- 
mann have shown that the state of equilibrium predicted for any material 
system is always the most probable state compatible with its total 
potential and kinetic energy. 

Hence we know theoretically, and it has been experimentally demon- 
strated in this book, that the proteins and other substances which con- 
stitute living matter have a tendency to concentrate at interfaces. 
They even carry with them part of the salts which, if alone in a solution, 
would show the opposite tendency. The precipitation or the coagula- 
tion of proteins may in certain cases be facilitated by this accumulation 
of the molecules. But a still more important conclusion can be drawn : 
i.e. that the most probable configuration of equilibrium of such a system 
is the cell form. 

It must be understood that the character of the probability which is 
referred to, indicates a mathematical probability of such a high degree, 

1 Lecomte du Noiiy, Science, 1926, LXIII, p. 284. 

187 



188 SURFACE EQUILIBRIA 

that up to a few years ago it was considered as an absolute necessity. 2 
In other words, the same idea can be expressed in the following way : 
the state of thermodynamic equilibrium of a system composed of 
proteins 3 in solution under the conditions stated above, is the cell form. 
Let us suppose that small droplets of a protein solution are projected 
into the atmosphere. Some may be of such dimensions as to stay in 
suspension for a few seconds at least before falling back into the liquid. 
According to the relation existing between the concentration of the 
proteins inside the droplet and the diameter, or better still, the ratio 

p:, different phenomena may occur; the larger droplets will not have 

reached an equilibrium, since the time required to do so evidently de- 
pends on the length of the path the molecule has to travel to reach the 
surface layer. Consequently they will not be coated with a homogeneous 
layer of proteins. When they fall back into the solution they are 
immediately disintegrated. Should they hit a dry surface, they would 
break up and evaporate, as their surface tension is not strong enough 
with respect to their mass to maintain their shape. 

On the contrary, among the smaller droplets there may be some of 
such diameter as to enable them to reach an equilibrium before falling 
back either into the solution or on a dry surface. These droplets will 
be coated with a surface layer of proteins 300 or 400 times more 
viscous than the interior, 4 which will give them a certain rigidity. 
Their mass being small, this layer will be strong enough to maintain 
their shape, even if they hit a dry surface, especially as they fall more 
slowly than the larger ones, and as the force of the impact is conse- 
quently much smaller. The presence of C0 2 , or HC1 gas, or ultra- 
violet rays, suffices to render some of the constituents of the protein 
layer insoluble, thus enabling the droplet to keep its individuality in the 
solution or in pure water. 

Let us now apply some of the figures obtained in our experiments 

'The reader will find it interesting to peruse two remarkable books on this 
subject: "La Physique depuis Vingt Ans," by Langevin, Paris, Doin, 1923; and 
"L'Evolution Physico-Chimique," by Ch. Eug. Guye, Paris, Chiron, 1923. 

3 Or any other organic substance of high molecular complexity endowed with 
the same properties with regard to surface tension. The term "protein" is used 
throughout this chapter for the sake of brevity, but the experimental facts and 
the hypothesis may apply as well to other compounds found in the cells and in 
the plasma, for instance, or to a combination of them. 

4 The experiments reported in Chapter 9, p. 176, show that even at a dilution 
of 1/10,000 the surface rigidity of serum is increased nearly 300 times in 90 
minutes. This concentration as well as the time are determined by the size and 
shape of the vessel. 



GENERAL CONCLUSIONS 189 

to this hypothesis. It has been shown (page 48) that the static value 
of surface tension in pure serum, for instance, is reached in about 20 
minutes in watch glasses where the depth of the liquid is about 3 mm. 
In the case of a spherical droplet of the same diameter, it would require 
about the same time to reach the equilibrium, that is to say, to coat it 
with a layer of concentrated proteins. But the same phenomenon 
would require only about 1 second if the droplet had a diameter 1000 
times less, — i.e. 3 \i, and about 4 seconds if its diameter were 10 \i. 
Consequently if a 6 per cent solution of proteins, such as the serum, 
were sprayed into an atmosphere containing C0 2 , for example, the 
droplets having a diameter of 10 \i, or less, would in 4 seconds be coated 
with a partly insoluble and very viscous layer which would transform 
them into individual cells. 5 

Furthermore, it has been shown that protein solutions under certain 
conditions of concentration, volume, and surface, could organize mono- 
layers at the interfaces (Chap. 3). The curves expressing the static 
values of surface tension of such solutions, drawn as a function of the 
concentration, show marked minima at certain critical concentrations. 
These minima, being due to a static arrangement of oriented, fixed mole- 
cules, cannot be accounted for on a thermodynamical basis. The Gibbs 
formula may enable us to calculate the static value of an egg albumin 
solution at a concentration 1/138,000 and at a concentration of 
1/142,000; but these points are on a smooth curve, and if, as happens, 
a minimum occurs between these two points, due to the organisation 
of molecules, no thermodynamic formula can, as yet, foresee this fact, 
which depends on the size and shape of the individual molecule. 6 Thus 
a sudden change may be expected in the surface tension at the interface 
between air and solution, or between two solutions, not necessarily 
as a consequence of a chemical reaction, as has always, so far, been 
assumed, but also as a consequence of a very slight change in the con- 
centration of either the outside or the inside liquid, according to whether 

5 This time of 4 seconds is a minimum based on the rate of the establishment 
of the equilibrium in pure serum. When dilute serum is considered the rate is 
slower, as has been shown in Chap. II. These figures should only be taken as 
an illustration of an order of magnitude and not as a quantitative expression of 
facts. 

6 Let us consider the diagram on Fig. 74. This curve expresses the static value 
of the surface tension of a protein solution as a function of concentration between 
A and B, which may differ from one another by as little as 10%. Let us con- 
sider 2 points on this curve, A' and B', very close to one another, and the position 
of which can be calculated by means of the Gibbs-Thomson equation. The 
formula will also enable us to calculate the points between A' and B' on a smooth 
curve, but not that of the point C. 



190 



SURFACE EQUILIBRIA 



the inside or the outside adsorbed layer is considered. A relative 
change in the concentration, of the order of 2/100 (from 1/138,000 
to 1/140,000, in our watch glasses, for instance), may bring forth a 
decrease of surface tension of a few dynes (3 to 8 in the case of egg 
albumin — air interface) on a limited area of the cell, if this change in 
concentration only affects part of the surrounding liquid. This area 
will, of course, immediately bulge out under the influence of the internal 
pressure, thus forming a pseudopod. 7 Changes in concentration of such 




Dilutions 
Fig. 74. 



an order of magnitude should be expected to go on almost continually 
under the influence of the slightest cause : foreign bodies adsorbing 
protein molecules, particles going into solution, etc. Changes in surface 
tension may be, therefore, considered as occurring constantly. 

The time required to organize such a layer over a limited area of a 
cell must be very small, if the concentration of the solution inside the 
cell is such as to make the formation of a monolayer possible. Indeed 
the aforesaid hypothesis requires one condition, i.e. that the concentra- 
tion and the adsorbing elements of the cell be related in a certain way. 
In our experiments monolayers were produced at dilutions around 
1/140,000 and 1/190,000 for egg albumin, and around 1/10,500 for 

serum (watch glasses)/ In these experiments the ratio — : , which 

7 A condenser is thus created and electro-capillary effects come into play. It 
is to be noted that it is necessary to admit the existence of some such action in 
order to account for the high efficiency of the organism as a machine. D'Arsonval 
was the first to suggest a similar explanation for muscular contraction. 



GENERAL CONCLUSIONS 191 

evidently determines for every concentration the possibility of forming 
the monolayer, was equal to 13.2 approximately. It is clear, as was 
pointed out in Chapter 3, that in order to obtain a monolayer forma- 
tion with pure serum, for instance, it would be necessary to use a much 
smaller vessel, shaped like a flat disc. A simple calculation shows that 
it should have such inside dimensions as, for instance, 5 u. in diameter 

S 
and 0.2 u in thickness ; in which case the ratio r- = 150,000. 

Under such conditions the formation of a monolayer with a concen- 
tration of proteins corresponding to that of pure serum, is possible 
from the inside. This calculation assumes, of course, that this cell 
contains no nucleus, or bodies capable of adsorbing the proteins (mito- 
chondria and others). In the latter case, the size of the cell could be 
larger without a concurrent decrease in the ratio. Should this ratio 
decrease, then a more dilute solution would be required to build up the 
monolayer ; should it increase by flattening of the cell or change in its 
shape, or should adsorbing bodies be formed inside the cell, a more 
concentrated solution would be necessary to build it. And reciprocally, 
if it be assumed that the size of the cell is determined somewhat by the 
possibility of forming, under certain conditions, oriented monolayers 
of proteins, the slightest change in the concentration — such as might be 
brought about by changes in the pH which affect the solubility of these 

substances — will determine a change in the ratio -== and the cell will 

grow or diminish in size, or alter its shape. Consequently the normal 
concentration of biological fluids might be one of the factors deter- 
mining the size of the living cells. Should our hypothesis be true, they 
could not exist outside of a certain range of dimensions, and their 
activity would depend, among other factors, on how near the critical 

s 

concentration they may be with respect to their ratio -r= . Indeed, if 

these three quantities happen to be balanced in such a way as to make 
the building of monolayers possible, they will be in a constant state 
of instability, as anything affecting the concentration may polarise the 
molecules on a certain area and change the surface tension, while in 
turn any phenomenon affecting the surface tension at one point will 

s 

determine a variation in the ratio -== which will result in a fluctuation 
in density in some other part of the cell, with a corresponding change 



192 SURFACE EQUILIBRIA 

in surface tension. 8 In certain cases, in which the externally adsorbed 
layer seems to be of constant thickness (red cells), the solid oriented 
layer of adsorbed serum proteins gives a certain rigidity to the cell. 
This adsorbed layer, the order of magnitude of which is about 40 
angstroms (40 X 10^ s cm.) is probably fixed on an inside layer, the 

thickness of which cannot be computed. Thus the ratio -^ of the inside 

of the cell may be larger than the outside ratio, and correspond to a 
higher concentration of proteins, not to mention the possibility of inside 
adsorbing elements. 

Our aim while writing this book was to remain on strictly experi- 
mental grounds and as far as possible only to mention those hypotheses 
which could be confirmed by simple and convincing experiments. These 
were always repeated a large number of times by different experimenters. 

During the course of the five years which were devoted to these 
researches, other hypotheses had to be made. Most of these will be 
found in the original papers. Although useful at the time, they were 
found later not to conform with all the experimental facts and had to 
be discarded. Such is the role of hypotheses in research. As Claude 
Bernard admirably expresses it : 9 

"Theories are as stepping stones of science, broadening its horizon 
at each advance, for the newer the theory, the more facts does it neces- 
sarily represent and include. Real progress consists in changing theories 
and taking new ones, which will go farther than the old ones, until one 
is found which will be established on a larger number of facts. . . . 
The important thing is to open up a new road." 

That is why we do not hesitate to end this book with a new hypothesis, 
which is nothing but an open door to other experimental researches, a 
question put to Nature. Whether new experiments invalidate or con- 
firm it matters little; in either case new facts will have been found, 
our knowledge will have progressed a little, and thus, whether discarded 
or accepted, its purpose will be achieved. We feel encouraged in this 
attitude by another paragraph of Claude Bernard's immortal book : 10 
"In short, even wrong hypotheses and theories are useful in leading to 
discoveries. This remark is true of all sciences. The alchemists 

8 It is usually admitted that the cell content is rather a concentrated solution 
of proteins. If this is true it becomes necessary to suppose that there is a 
considerable surface of adsorption inside the cell, in addition to those which can 
be seen under the microscope. 

8 Claude Bernard. Introduction a l'etude de la medicine experimentale, p. 263. 

10 Claude Bernard. Loc. cit., p. 272. 



GENERAL CONCLUSIONS 193 

founded chemistry while pursuing chimerical problems and theories 
which have been found erroneous to-day. In the physical sciences, more 
advanced than biology, scientists could be cited even now, who are 
making great discoveries although starting from a wrong theory. It 
seems indeed a necessity of the weakness of our mind that we cannot 
attain truth except by passing through a multitude of errors and perils." 



Bibliography 

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The following bibliography is far from being complete. But most 
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Serum. (Uber physikalisch-chemische Anderungen im Serum als Folge 
der Immunisierung, Biochcm. Z., 1925, clxv, 134. Studi sperimentali 
sulla tensione superficiale del siero, Biochimica e Terapia Spcrimentale, 
1925. 

Leduc, S., and Sacerdote, I. Sur la cohesion des liquides, Compt. 
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Lehman, O. Die Quellung fliissiger Kristalle. Dcutsch. pliysik. Ges., 
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Linebarger, C. E. On the relations between the surface tensions of 
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3, 83. 

Loeb, J. The dynamics of living matter, Columbia University Bio- 
logical Series 8, New York, 1906. 



BIBLIOGRAPHY 199 

Lohnstein, I. Nochmals das sogenannte Gesetz von Tate, Z. physik. 
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Lynde, C. J. The effect of pressure on surface tension, Chicago, 
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Maass, O. Measurement of surface tension by means of a vertical 
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Macallum, A. B. A study on the action of surface tension in deter- 
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Madelung, E. Kinetische Theorie des Gesetzes von Eotvos, Z. 
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200 BIBLIOGRAPHY 

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202 BIBLIOGRAPHY 

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TABLE OF FIGURES AND PLATES 



FIGURES 

FIG. PAGE 

1 View of the Tensiometer 24 

2 Set up of the electrical connection of the tensiometer to the kymograph 40 

3 Decrease of the surface tension of serum as a function of time ... 41 

4 Decrease of the surface tension of serum as a function of time ... 42 

5 Decrease of the surface tension of sodium oleate solutions as a func- 

tion of time 43 

6 Rate of decrease of the surface tension of serum 44 

7 Modification of the surface tension of serum as a function of time . . 48 

8 Effect of stirring on the surface tension of serum 48 

9 Effect of stirring on the surface tension of serum . 49 

10 Action on the surface tension of the adsorption of sodium glycocholate 

by paraffin oil 50 

11 Action on the surface tension of adsorption in the surface layer of serum 50 

12 Effect of stirring on solutions of serum 51 

13 Action of temperature on the dynamic value of surface tension of serum 53 

14 Action of temperature on the surface tension of serum — mean values 53 

15 Action of temperature on the static value of surface tension of serum 

(mean curves) 55 

16 Action of temperature on the time-drop of serum — mean values . . 55 

17 Temperature coefficient of pure serum 56 

18 Time-drop in two hours as a function of the concentration, at different 

temperatures 56 

19 Static and dynamic surface tension of serum dried and redissolved 

in water 63 

20 Static and dynamic surface tension of serum dried in C0 2 atmosphere 

and redissolved in water 63 

21 Same experiment under nitrogen 63 

22 Time-drop of serum solutions 64 

23 Values of the surface tension of serum solutions as a function of time 65 

24 Values of the surface tension of serum solutions as a function of time 65 

25 Drop in the surface tension of different solutions as expressed by: 

— ay = Yo — 7 66 

26 Action of salts (NaCl) on the surface tension of sodium oleate solu- 

tions, at different concentrations 67 

27 Action of NaCl on the time-drop of sodium oleate 67 

28 Action of NaCl on the time-drop of sodium glycocholate solutions at 

different concentrations 68 

203 



204 TABLE OF FIGURES AND PLATES 

FIG. PAGE 

29 Surface tension of serum solutions. Initial value and value after 2 

hours. (Dynamic and static) 68 

30 Diameter of serum solutions in watch glasses after a few hours evapora- 

tion 71 

31 Shift in the minimum value of static surface tension as a consequence 

of the increase of the surface of adsorption 78 

S 

32 Shift of the minimum due to a decrease in the ratio ~- (serum) . . 80 

S 

33 Shift of the minimum due to an increase of the ratio-Try- — (Sodium 

oleate) 86 

34 Shift of the three minima of sodium oleate due to a decrease in the 

ratio -ry Expt. No. 1 ... . 87 

35 Shift of the three minima of sodium oleate due to a decrease in the 

ratio rr= Expt. No. 2 87 

36 Shift of the three minima of sodium oleate due to a decrease in the 

ratio -^ Expt. No. 3 . . . 87 

37 Shift of the three minima of sodium oleate due to a decrease in the 

ratio t— Expt. No. 4 88 

38 Dynamic and static values of the surface tension of sodium oleate solu- 

tions, at concentrations ranging from 1/1,000 to 1/3,000,000 ... 91 

39 Shape of Sodium Oleate Molecule 97 

40 Static surface tension of Egg Albumin solution 107 

41 Static surface tension of Egg Albumin solution . 108 

42 Static surface tension of Egg Albumin solution 109 

43 Static surface tension of Egg Albumin solution 110 

44 Static surface tension of Egg Albumin solution Ill 

45 Static surface tension of Egg Albumin solution 112 

46 Frequency of occurrence of minima 113 

47 Phantom shape of molecule 116 

48 Time-drop curves, before and after immunization 123 

49 Time-drop before and after immunization 123 

50 Curve representing the evolution of the process of immunization as a 

function of time 124 

51 Curve representing the evolution of the process of immunization as a 

function of time 125 

52 Curve representing the evolution- of the process of immunization as a 

function of time 125 

53 Static value of immune and normal serum 131 

54 Static value of immune and normal serum . 134 

55 Static value of immune and normal serum 135 

56 Static value of immune and normal serum 136 

57 Static value of immune and normal serum 137 



TABLE OF FIGURES AND PLATES 205 

FIG. PAGE 

58 Time-drop after two hours of immune and normal serum .... 138 

59 Static values, after 2 hours, of normal rabbit serum 139 

60 Mean value of initial surface tension before and after immunization . 140 

61 Recovery of surface tension of serum to which sodium oleate has been 

added 156 

62 Recovery of surface tension of colloidal gold solution to which sodium 

oleate has been added 158 

63 Recovery of surface tension of colloidal gold and glycerin solution to 

which sodium oleate has been added 158 

64 Recovery of surface tension of gum arabic solution after addition of 

sodium oleate 159 

65 Recovery of surface tension of serum and serum solutions after addi- 

tion of sodium oleate 160 

66 Recovery of surface tension of serum solutions after addition of differ- 

ent amounts of sodium oleate 161 

67 Semilogarithmic recovery of serum solutions after addition of sodium 

oleate 162 

68 Recovery of surface tension of serum solution after heating five minutes 

at 100° C . 163 

69 Action of sodium oleate on surface tension of water prevented by pres- 

ence of another colloid 165 

70 Design of the Interfacial Tensiometer 168 

71 Interfacial Tensions of Water- Carbon disulphide interface, as a func- 

tion of temperature 173 

72 Interfacial Tension Sodium oleate solutions — Paraffin Oil ..... 174 

73 Surface Viscosity of a serum solution as a function of time . . . 176 

74 Schematic diagram of the static surface tension of a protein solution . 190 



PLATES 

PLATE PAGE 

I Apparatus for measuring the static value of the surface tension 

of series of solutions 34 

II Action of temperature on the crystallisation of serum solutions, 

at 1/10 in saline solution 57 

III Photomicrograph of a drop of serum diluted to 1/10 in saline 

solution — Room temperature 58 

IV Photomicrograph of a drop of serum diluted to 1/10 in saline 

solution — Kept at 55° for two hours 59 

V Photomicrograph of a drop of serum diluted to 1/10 in saline 

solution — Kept at 70° for one hour 60 

VI Photomicrograph of a drop of serum diluted to 1/10 in saline 

solution — Kept at 100° for five minutes 61 

VII Setting for the study of the action of gases 62 

VIII Study of the rate of evaporation on plane glass. Aspect of 

crystals of NaCl 74 



206 



TABLE OF FIGURES AND PLATES 



PLATE PAGE 

IX Aspect of crystallization of normal and immune serum solutions 

on watch glasses, after evaporation 142 

X Photomicrographs of areas delimited in black on plate IX . 143 

XI Crystals of serum solutions in NaCl solution at 0.9 per cent. 

(Rabbit) 146 

XII Crystals of serum solutions in NaCl solution at 0.9 per cent 

(Rabbit) 148 

XIII Crystals of Saponin solutions in NaCl solution at 0.9 per cent . 149 

XIV NaCl solution 0.9 per cent evaporated at room temperature in 

watch glasses 150 

XV Serum solutions evaporated under different gases 151 

XVI Sodium Oleate in 0.9 per cent NaCl solution, evaporated at room 

temperature 152 

XVII Sodium Oleate in 0.9 per cent NaCl solution, evaporated at room 

temperature. 153 

XVIII Fig. I Interfacial Tensiometer. Fig. II Appearance of interface 

deformed by the ring 167 

XIX Plasma (chicken) pure. Dark ground, Zeiss paraboloid condenser 181 
XX Serum (rabbit) pure. Dark ground, Zeiss paraboloid condenser 181 
XXI Sugar solution (glucose) 20 per cent, unfiltered. Dark ground, 

Zeiss paraboloid condenser 182 

XXII Sugar solution (glucose) 20 per cent, filtered through Berkefeld 

filter. Dark ground, Zeiss paraboloid condenser 182 



AUTHOR INDEX 



(This list contains only the names quoted in the book and not those 
mentioned in the bibliography.) 



Adam, N. K., 98 
Alexander, J., 179 
Arsonval, d'A., 190 
Arthus, M., 80 
Ascoli, M., 120 
Avogadro, 86, 100, 103 

B 

Bailey, G. H, 120 
Baker, L. E., 89, 120, 140 
Bayliss, W. M., 21, 22 
Bechhold, H., 183 
Berger, W., 120 
Bernard, CI., 19, 192 
Bernstein, J., 55 
Bohr, N., 28 
Boltwood, 103 
Boltzmann, 187 
Brillouin, M., 103 
Broglie, de, L., 99 
Brown, F. E., 166 
Brown, J. G., 83 



Cabannes, J., 180 

Cantor, M., 27, 28 

Cheng, W. C, 166 

Chwolson, O. D., 21 

Clark, H., 162 

Cohn, E. J., 106, 115, 179, 186 

Curie, M., 103 

D 

Danzer, C. S., 83 
Davies, E. C. H., 166 
Devaux, H., 30, 97, 98 
Doerr, R., 120 
Dorsey, N. E., 28 



Einstein, A., 19 
Evans, F. A., 162 



Felton, L. D., 120 
Ferguson, A., 21 



Fischer, A., 124^ 
Fletcher, H., 103 
Freundlich, H., 28, 47 
Fricke, H., 85, 183 



Gautier, A., 106 

Gibbs, W., 21, 76, 145, 187, 189 

Graham, 179 

Griffin, E. L., 89, 99 

Guye, Ch. E., 188 

H 

Hall, P., 28 

Hardv, -W. B„ 85 

Harkins, W. D., 89, 98, 99, 166, 171 

Heidelberger, M., 106 

FTendry, J. L., 106 

Hitchcock. D., 186 

Holmes, H. N., 21 

Hooker, D. R, 83 

Horowitz, K., 147, 151 

J 

Jaeger, F. M., 21, 23, 28 
Jorgensen, A., 124 

K 

Kahn, R. H., 83 
Kalahne, A., 28 
Kenrick, F. B., 180 
King, 103 

Klopsteg, P. E., 27, 28, 29 
Kohlschtitter, V., 145 
Krogh, A., 83 

L 

Lambling, E., 106 

Landsteiner, K.. 129 

Langevin, P., 188 

Langmuir, I., 46, 97, 98, 99, 118 

Lecomte du Noiiy, P., 21, 28, 39, 47, 
52, 62, 66, 72, 76, 82, 85, 89, 103, 
120, 122, 140, 155, 163, 166, 175, 
179, 187 

Lehrman, S., 180 

Lenard, P., 28 



207 



208 



AUTHOR INDEX 



Lewis, W. G McC, 49, 50 
Liesegang, R. E., 147 
Lobry de Bruyn, C. A., 179 
Loeb, J., 178, 183, 186 
Lohnstein, T., 28 
Lorentz, II. A.. 103 
Lumiere, A.. 184. 186 



Ramsden. W., 52 
Raoult, 75 

Ravleigh, Lord, 28, 98, 180 
Roy, C. S, 83 
Rutherford, Sir E., 103 



M 

Macallum, A. B., 147 
Madsen, T., 124 
Magini, R., 28 
Marcelin, A., 98, 99 
Martin, W. H., 179 
Mathews, A. P., 80, 106 
Mathieu, J.. 23 
Maxwell, J. C, 19 
Alillikan. R. A., 100, 103 
Muller, A., 99 



Newton, I.. 19 
Noguchi, H., 126 
Nortbrup, J., 186 



N 







Ollivier, H., 28 

Osborne, T. B., 104, 106, 118 



Pacini, 103 
Pasteur, L., 19 
Pedersen. P., 28 
Perrin, J., 103 
Planck. M., 103 
Pockels, A., 98 
Prentiss. A. M.. 106 
Prillat. J. J., 99 



Quincke, M. G., 171 



Seith, W., 66 

Shearer, G., 99 

Sondhaus, C., 23 

S6rensen, S. P. L., 106, 115, 118, 179, 

180. 183 
Spear, E. B., 179 
Steinach, E., 83 
Svedberg, T., 103 



Tavlor, W. W., 35 
Thomson, J. J., 76, 187, 189 
Timberg, G., 23, 27, 28 
Tyndall, 178 

V 



Vigneron, H., 21 
Villa, L., 183 
Volkman, 28 



W 



Waterman, N., 120 
Weinberg, B., 23, 27, 28 
Wells, H. G., 163, 184 
Westgren, A., 103 
Wijs, 90 
Wollstein, M., 128 



Zinck, R. H., 162 
Zollman, H., 89, 99 
Zsigmondy, R., 147, 179, 185 
Zwick, T., 28, 91 



SUBJECT INDEX 



Absolute values of surface tension, 26, 

27 
Acids, fatty, 98; in serum, 121 
Adsorption, in the surface layer, 21, 
22,96 
on the glass, 77 to 80 ; and 86 to 89 
of one colloid by another, 158, 159, 

etc. 
at interfaces, 174 
of salts, 145 
formula, 46 
rate of, 42, 43, 44, 47 
area of adsorbing surfaces, 77, 78, 

etc. ; 86 to 89 
curves, isotherms, 41, 42, 43, 48, 50, 

174 
of proteins by red cells and capil- 
laries, 82, 83, 84 
Ageing of colloidal solutions, 49, 50, 

183 
Agglutination, 84 
Albumin (See Egg and Serum) 
Alcohol, isoamyl, octyl, benzyl, inter- 
facial tension against water, 169 
Alizarin red, 38 
Alkali blue, 36 ; 
Amicrons, polarization by, 179 
Amino-acids, in the serum, 81 
Amoeba, ameboid motion, 190 
Anilin, dimethyl, diethyl, interfacial 

tension against water, 169 
Antagonistic effect, 155 
Arsenious sulphide, 35 
Auramine, 38 
Avogadro constant, calculation, 100 

principal determinations, 104 
Azo blue, 36 

B 

Bacillus coli. 126, 140 
Benzene, 169 
Benzo Azurine, 38 

purpurine, 38 
Bismarck brown, 38 
Blood (See Serum and Plasma) 

red cells used as antigen, 122 

protein adsorbed on red cells from 
the. 84, 192 

red cells, agglutination, 84 



Bredig's method, metallic sols, 52 
Bromoform, 169 
Brownian movement, 178, 179 
in sugar solutions, 180 



Capillarity, influence on crystalliza- 
tion, 145 

Capillary ascension method, 21, 23 

Carbon, bisulphide, interfacial tension, 
and temperature coefficient, 169, 
173 
dioxide, action on surface tension, 

63; on crystallisation, 151 
tetrachloride, interfacial tension 
against water, 169 

Carmine, 36 

Castor oil, interfacial tension against 
water, 169 

Cells, study of ratio sl ^ face 82; 188 
volume 

to 192 

Chloroform, interfacial tension against 

water, 169 

Cholesterol, 121 

Cleaning solution, 29 

of glassware, 29 
Colloidoclasie, 184 
Colloids and colloidal state, 178 

in biology and medicine, 184, 187 

dyes, 36 
Complement, destruction by heat, 55 
Concentration of the serum, signifi- 
cance, 82 
Congo brown, 36 

red, 36 
Crystallization, influence of colloids 

on, 57 to 61 ; 145 
Crystalloids, dyes, 38 
Cysteine, 105 
Cystine, 105 



Diamine blue, 37 
Diamine green, 36 
Dilution, effect of, 64, 67 
Drop weight methods, 21, 22 
Dyestuffs, dynamic and static surface 
tension of sols, 35, 36, 37, 38 



209 



210 



SUBJECT INDEX 



Dynamic value of surface tension, 
definition and measurement, 21, 
22, 45 



Egg albumin, 105 

surface tension of solutions, 10/ to 

112 
preparation, 106 
constitution, 105, 106 
sulphur content, 105, 106 
molecular weight from sulphur 

content, 106 
molecular dimensions, 114, 115, 118 
molecular weight from molecular 

dimensions, 114, 115 
specific gravity, 114, 116 
colloidality, 178, 179, 183 
Elaidate, sodium, 89 
Eosin, 38 
Equilibrium in colloidal solutions, 22, 

45, 46, 50, 76, 89 ; 188 
Equilibrium between two colloids in 

solution, 
Errors, principal sources of, 29, 31, 39 
Erythrocytes (See red corpuscles) 
Ethyl, ether, carbonate, iodide, phta- 
late, interfacial tensions against 
water, 169 
Evaporation, rate of, 71 to 75 



Fats, 121 

Fatty acids, 46, 121 

Ferric hydroxide, 35 

Film at the surface of colloidal solu- 
tions, 52, 70 

Flaming of the glass, influence on the 
wetting, 30; on crystallization, 
150 

Fluorescein, 38 

Fuchsin, 37 

G 

Gases, action on surface tension of 

colloidal solutions, 62 

Gibbs-Thomson's law, 21, 76, 145, 187, 

189 

Glass, adsorption by, 77 to 80; 86 to 

89 

differences between, with respect to 

adsorption and crystallization, 150 

cleaning, 29 

flaming, 30, 150 

wetting, 30 

old and new, 150 

~. . .. . albumin . 

Globulin, ratio : -=-« — r- — after lm- 



Gold, colloidal, adsorption as a func- 
tion of time, 52 
antagonistic action, 158 
action of heat, 52 
surface tension, 52 
adsorption of another colloid by 
t gold particles, 158 
size of particles, 179 
Gum Arabic, adsorption by, 159 

H 

Hanging drops methods, 22 
Heat, action of, 52; at interfaces 
water - carbon - bisulphide, and 
water-ethyl-ether, 172 
Hemoglobin, 66 

size of molecule, 179 
Hemolysis, 84 

Human serum, immune and normal, 
128 

I 
Induline, 37 
Influence of gases, 62 
Influence of time, 35 
heat, 52 to 62; at interfaces, 171, 

172 
stirring, 47 to 52 
traces of impurity, 164, 165 
incomplete wetting of watch glasses, 
30 
Inoculation, 122, 129 
Interfacial tension, 166 
Isotonic solution sodium chloride, 
preparation, 31 



Jaundice, protection from hemolytic 
action of bile salts, 158 

K 

Kjeldahl, determination of nitrogen 
content of serum, 80 



Lecithin, 121 

Light scattering by particles, 179 

Lipoids, 76, 85 



munization, 141 



globulins 



M 



Manganese dioxide, 35 
Meiostagmin reaction, 120 
Membrane, red cells, thickness, 85, 

192 
Metals, colloidal, time-drop, 52 

antagonistic effect, 158 
Methods of measurement of surface 

tension, 21, 39, etc. 



SUBJECT INDEX 



211 



Methylene blue, 38 

Micellae, proportion of, in serum and 

plasma, 183 to 185 
Minima of static value .of surface 

tension, 68, 69, 78, 86, 90, etc. 
Molecules (See specific subject), 
size, dto., ratio to micellae in plasma 
and serum, 183 to 185 
Monomolecular layers, hypothesis, 69 ; 
96 
of serum constituents, 56, 71, 81 
of egg albumin, 113 to 115 
of sodium oleate, 96 
in cells, 84; 189 
around red corpuscles, 83, 84; 192 



Q 

Quartz, adsorption on, 147 



R 



Red corpuscles as antigen, 122 

adsorption on, 83, 84, 192 
Refractive index of serum, normal 

and immune, 141, 144 
Relative values of surface tension, 28 
Rhodamine, 38 
Ring method, 21, 23, 27 

dimensions of, 23 



N 

Naphthol, yellow, 37 
Neutral red, 37 
Night blue, 37 
Nile blue, 37 _ 

Nitrogen, action on surface tension, 
63 

O 

Oleic acid, dimension of molecule, 97, 
98,99 

Octyl alcohol, oleic acid, olive oil, in- 
terfacial tension against water, 
169 

Orientation of molecules in mono- 
layers, 45; 97; 113, etc. 

Osmotic pressure, albumin, 120 



Paraffin oil, interfacial tension against 
water, 169, 174 

sodium oleate solutions, 174 
Particles, size of, 179, 180, 183 

number of, 185 

Brownian movement, 178, 180 
Physiological solution, preparation, 31 
Petrolatum, liquid, 169 
Plasma, colloidality of, 178 
Polarisation of molecules in mono- 
layers, 69, 71, 96; 191 

around red cells, 84 ; 192 
Precipitation in serum, influence on 

surface tension, 51 
Protection effect, 162 
Proteins, serum, 80 to 85 

solutions from thermodynamical 
standpoint, 187 

specific gravity, serum, 80 

sensitization, 122 

detection of traces of, 163 

colloidality of solutions of, 178 

(See Egg Albumin). 



Safranine, 38 
Salts, colloidal, 35 

effect on time-drop, 66 

crystallization, 142, 145 

adsorption of, 145 
Semi-colloids, dyes, 37 
Serum, blood, monomolecular layer, 
71, 76 

concentration in proteins, 80 

characteristics of immune serum, 
120 
Silver, colloidal, time-drop, 52 
Snuffles in rabbits, 128 
Soap (see sodium oleate) 
Sodium chloride, purification, 31 

crystals, 57, 142, 145 

glycocholate, 50, 66, 68 
Sodium oleate, surface tension, 22 

surface tension, minima, 91 to 96 

surface tension, shift of minima, 86 
to 88 

preparation, 90 

importance of purity, 89 

dimension of molecule, 97 

and the Avogadro constant, 100 

preservation, 90 

preparation of solutions, 32 
Solutions, colloidal, positive adsorp- 
tion, Chapters 2 and 9 

adsorption on glass, 77, 86 

adsorption at interfaces, 174 

action of time, 35 

action of heat, 52; at interfaces, 
172, 173 

mutual adsorption, 155, 156, etc. 

colloidality, 178 

preparation, 30, 32 
Specific gravity of anhydrous pro- 
teins, 80 > 

e^fc albumin, 114 

sodium oleate, 97 
Standardisation of tensiometer, 24, 25 
Starch, size of molecule, 178 



212 



SUBJECT INDEX 



Stirring, action of, 47 

Stalagmometric methods, 22 

Static value of surface tension, defi- 
nition, measurement, 23, 33, 34, 
35 

Sugar, ultramicroscopic aspect of so- 
lutions, 181, 182 

c , £ surface 

Surface, importance of ratio, — : 

volume 

47. 76, 82. 88 
tension (See specific subject) ; 

measurements, Chaps. 1 and 2 
tension of water, 28 
viscosity, 166 



Toluene, interfacial tension against 

water, 169 
Turpentine interfacial tension against 

water, 169 
used as nonantigenic substance for 

controls, 122, 125 
Tyndall effect, 89, 178 

U 

Ultramicroscopv, study of colloids, 
181, 182, 185 
counting of micellae, 185 
photographs, 181, 182 



Technique, surface tension measure- 
ments, 26 to 34-39 

Temperature, effect on colloidal solu- 
tions, 52, etc. 
coefficient at interfaces, 172, 173 
effect on the crystallization of com- 
pound solutions, 57 to 61 

Tensiometer, description, 23, 24. In- 
terfacial, 167, 168 

Thermodvnamics of cell formation, 

Thionine, 38 

Time, influence of, 22, 35; 174; 176 
Time-drop, definition, 54, 64 



Vaccine and time-drop, 126, 127 
Violet black, 37 
Viscosity, surface, 52; 174 
Volume, its importance with respect 

to surface, 47, 76, 82, 88; 188, 

etc. 

W 

Washing of glasses, 29 
Water, necessity of clean, 31 
Watch glasses, specifications of stand- 
ard, 33 
Wetting of the ring, 26 
Wetting of surfaces, 29, 30 



Xvlene-m, 169